Use common logarithms or natural logarithms and a calculator to evaluate the expression.
$\log_{18} 16$
Use the change-of-base property to rewrite the given expression in terms of natural logarithms or common logarithms. $\log_{18} 16 =$
(Do not evaluate.)

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Answer

$\log_{18} 16 = \frac{\ln 16}{\ln 18}$ or $\log_{18} 16 = \frac{\log 16}{\log 18}$

Steps

Step 1 ：Given the expression $\log_{18} 16$

Step 2 ：We can use the change-of-base property to rewrite the given expression in terms of natural logarithms or common logarithms. The change-of-base formula is $\log_{b} a = \frac{\log_{k} a}{\log_{k} b}$ , where k can be any positive number except 1.

Step 3 ：Using this formula, we can rewrite the expression $\log_{18} 16$ as follows:

Step 4 ：Using natural logarithms (base e): $\log_{18} 16 = \frac{\ln 16}{\ln 18}$

Step 5 ：Using common logarithms (base 10): $\log_{18} 16 = \frac{\log 16}{\log 18}$

Step 6 ： $\log_{18} 16 = \frac{\ln 16}{\ln 18}$ or $\log_{18} 16 = \frac{\log 16}{\log 18}$

Use common logarithms or natural logarithms and a calculator to evaluate the expression.log18⁡16Use the change-of-base property to rewrite the given expression in terms of natural logarithms or common logarithms. log18⁡16=(Do not evaluate.)

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Popular Problems

Use common logarithms or natural logarithms and a calculator to evaluate the expression.
$\log_{18} 16$
Use the change-of-base property to rewrite the given expression in terms of natural logarithms or common logarithms. $\log_{18} 16 =$
(Do not evaluate.)