Using Logarithms with Exponents - Math

Card 1 of 16

Didn't Know

Knew It

1 of 1615 left

Question

Evaluate by hand $\log_$2(4^{\log_2(4^{5}$)})$

Tap to reveal answer

Answer

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as $5\log_2(4)\log_2(4)$

← Didn't Know|Knew It →

Question

Solve for

Tap to reveal answer

Answer

Use the power reducing theorem:

$\log $a^x$ = b \rightarrow x\log a = b$

and

$x\log 2 = 6$

$x= $\frac{6}{\log 2}$$

← Didn't Know|Knew It →

Question

Which of the following expressions is equivalent to ?

Tap to reveal answer

Answer

According to the rule for exponents of logarithms,. As a direct application of this,.

← Didn't Know|Knew It →

Question

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Tap to reveal answer

Answer

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log $(2^{3}$)$ .

Then, we use the following rule of logarithms:

Thus, .

← Didn't Know|Knew It →

Question

Evaluate by hand $\log_$2(4^{\log_2(4^{5}$)})$

Tap to reveal answer

Answer

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as $5\log_2(4)\log_2(4)$

← Didn't Know|Knew It →

Question

Solve for

Tap to reveal answer

Answer

Use the power reducing theorem:

$\log $a^x$ = b \rightarrow x\log a = b$

and

$x\log 2 = 6$

$x= $\frac{6}{\log 2}$$

← Didn't Know|Knew It →

Question

Which of the following expressions is equivalent to ?

Tap to reveal answer

Answer

According to the rule for exponents of logarithms,. As a direct application of this,.

← Didn't Know|Knew It →

Question

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Tap to reveal answer

Answer

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log $(2^{3}$)$ .

Then, we use the following rule of logarithms:

Thus, .

← Didn't Know|Knew It →

Question

Evaluate by hand $\log_$2(4^{\log_2(4^{5}$)})$

Tap to reveal answer

Answer

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as $5\log_2(4)\log_2(4)$

← Didn't Know|Knew It →

Question

Solve for

Tap to reveal answer

Answer

Use the power reducing theorem:

$\log $a^x$ = b \rightarrow x\log a = b$

and

$x\log 2 = 6$

$x= $\frac{6}{\log 2}$$

← Didn't Know|Knew It →

Question

Which of the following expressions is equivalent to ?

Tap to reveal answer

Answer

According to the rule for exponents of logarithms,. As a direct application of this,.

← Didn't Know|Knew It →

Question

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Tap to reveal answer

Answer

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log $(2^{3}$)$ .

Then, we use the following rule of logarithms:

Thus, .

← Didn't Know|Knew It →

Question

Evaluate by hand $\log_$2(4^{\log_2(4^{5}$)})$

Tap to reveal answer

Answer

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as $5\log_2(4)\log_2(4)$

← Didn't Know|Knew It →

Question

Solve for

Tap to reveal answer

Answer

Use the power reducing theorem:

$\log $a^x$ = b \rightarrow x\log a = b$

and

$x\log 2 = 6$

$x= $\frac{6}{\log 2}$$

← Didn't Know|Knew It →

Question

Which of the following expressions is equivalent to ?

Tap to reveal answer

Answer

According to the rule for exponents of logarithms,. As a direct application of this,.

← Didn't Know|Knew It →

Question

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Tap to reveal answer

Answer

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log $(2^{3}$)$ .

Then, we use the following rule of logarithms:

Thus, .

← Didn't Know|Knew It →

Knew It

Using Logarithms with Exponents - Math

Evaluate by hand

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as

Solve for

Use the power reducing theorem: and

Which of the following expressions is equivalent to ?

According to the rule for exponents of logarithms,. As a direct application of this,.

Simplify the expression below.

Based on the definition of exponents, . Then, we use the following rule of logarithms: Thus, .

Evaluate by hand

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as

Solve for

Use the power reducing theorem: and

Which of the following expressions is equivalent to ?

According to the rule for exponents of logarithms,. As a direct application of this,.

Simplify the expression below.

Based on the definition of exponents, . Then, we use the following rule of logarithms: Thus, .

Evaluate by hand

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as

Solve for

Use the power reducing theorem: and

Which of the following expressions is equivalent to ?

According to the rule for exponents of logarithms,. As a direct application of this,.

Simplify the expression below.

Based on the definition of exponents, . Then, we use the following rule of logarithms: Thus, .

Evaluate by hand

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as

Solve for

Use the power reducing theorem: and

Which of the following expressions is equivalent to ?

According to the rule for exponents of logarithms,. As a direct application of this,.

Simplify the expression below.

Based on the definition of exponents, . Then, we use the following rule of logarithms: Thus, .

Evaluate by hand $\log_$2(4^{\log_2(4^{5}$)})$

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as $5\log_2(4)\log_2(4)$

Use the power reducing theorem:

$\log $a^x$ = b \rightarrow x\log a = b$

and

$x\log 2 = 6$

$x= $\frac{6}{\log 2}$$

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log $(2^{3}$)$ .

Then, we use the following rule of logarithms:

Thus, .

Evaluate by hand $\log_$2(4^{\log_2(4^{5}$)})$

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as $5\log_2(4)\log_2(4)$

Use the power reducing theorem:

$\log $a^x$ = b \rightarrow x\log a = b$

and

$x\log 2 = 6$

$x= $\frac{6}{\log 2}$$

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log $(2^{3}$)$ .

Then, we use the following rule of logarithms:

Thus, .

Evaluate by hand $\log_$2(4^{\log_2(4^{5}$)})$

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as $5\log_2(4)\log_2(4)$

Use the power reducing theorem:

$\log $a^x$ = b \rightarrow x\log a = b$

and

$x\log 2 = 6$

$x= $\frac{6}{\log 2}$$

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log $(2^{3}$)$ .

Then, we use the following rule of logarithms:

Thus, .

Evaluate by hand $\log_$2(4^{\log_2(4^{5}$)})$

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as $5\log_2(4)\log_2(4)$

Use the power reducing theorem:

$\log $a^x$ = b \rightarrow x\log a = b$

and

$x\log 2 = 6$

$x= $\frac{6}{\log 2}$$

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log $(2^{3}$)$ .

Then, we use the following rule of logarithms:

Thus, .