## Example Questions

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### Example Question #1 : Logarithms

Let log 5 = 0.69897 and log 2 = 0.30103.  Solve log 50

1.69897

1.36903

1.39794

1.68794

1.30103

1.69897

Explanation:

Using properties of logs:

log (xy) = log x + log y

log (xn) = n log x

log 10 = 1

So log 50 = log (10 * 5) = log 10 + log 5 = 1 + 0.69897 = 1.69897

### Example Question #1 : Logarithms

y = 2x

If y = 3, approximately what is x?

Round to 4 decimal places.

1.3454

2.0000

1.8580

1.5850

0.6309

1.5850

Explanation:

To solve, we use logarithms. We log both sides and get: log3 = log2x

which can be rewritten as log3 = xlog2

Then we solve for x: x = log 3/log 2 = 1.5850 . . .

### Example Question #1 : How To Find A Logarithm

Evaluate

log327

10

3

9

27

30

3

Explanation:

You can change the form to

3x = 27

= 3

### Example Question #1 : Logarithms

If , what is ?      Explanation:

If , then   ### Example Question #1 : Logarithms

If log4  x = 2, what is the square root of x?

12

16

4

2

3

4

Explanation:

Given log4= 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.

### Example Question #1 : How To Find A Logarithm

Solve for x in the following equation:

log224 - log23 = logx27

9

1

3

2

2

3

Explanation:

Since the two logarithmic expressions on the left side of the equation have the same base, you can use the quotient rule to re-express them as the following:

log224  log23 = log2(24/3) = log28 = 3

Therefore we have the following equivalent expressions, from which it can be deduced that x = 3.

logx27 = 3

x3 = 27

### Example Question #1 : Logarithms

What value of satisfies the equation ?      Explanation:

The answer is . can by rewritten as .

In this form the question becomes a simple exponent problem. The answer is because .

### Example Question #3 : Logarithms

If , what is ?      Explanation:

Use the following equation to easily manipulate all similar logs: changes to .

Therefore, changes to .

2 raised to the power of 6 yields 64, so must equal 6. If finding the 6 was difficult from the formula, simply keep multiplying 2 by itself until you reach 64.

### Example Question #1 : How To Find A Logarithm

Which of the following is a value of that satisfies ?      Explanation:

The general equation of a logarithm is , and In this case, , and thus (or , but is not an answer choice)

### Example Question #1 : How To Find A Logarithm

How can we simplify this expression below into a single logarithm?    Cannot be simplified into a single logarithm  Explanation:

Using the property that , we can simplify the expression to .

Given that and We can further simplify this equation to ← Previous 1 3

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