Using Natural Log and Log-Base-10

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Math › Using Natural Log and Log-Base-10

Questions 1 - 3

1

Based on the definition of logarithms, what is ${\log_{10}1000}$ ?

3

100

10

2

4

Explanation

For any equation $\log_{10}(y) = x$ , $10^{x } = y$ . Thus, we are trying to determine what power of 10 is 1000. , so our answer is 3.

2

What is the value of that satisfies the equation $\log_x128=7$ ?

$\frac{1}{2}$

Explanation

$\log_xa=b$ is equivalent to . In this case, you know the value of (the argument of a logarithmic equation) and b (the answer to the logarithmic equation). You must find a solution for the base.

$x^{7}=128$

$\sqrt[7]{x}=\sqrt[7]{128}$

3

$\log_7118=?$

Explanation

Most of us don't know what the exponent would be if and unfortunately there is no $\log_7$ on a graphing calculator -- only $\log$ (which stands for $\log_{10}$ ).

Fortunately we can use the base change rule: $\log_ba=\frac{\log_{10}a}{\log_{10}b}$

Plug in our given values.

$\log_7118=\frac{\log_{10}118}{\log_{10}7}$

$\log_7118=\frac{2.07}{0.845}$

$\log_7118=2.45$

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