Use common logarithms or natural logarithms and a calculator to evaluate the expression. $$ \begin{array}{l}\log _{18} 19 \ ext { Use the change-of-base property to rewrite the given } \ ext { expression in terms of natural logarithms or common } \ \operatorname{logarithms.~} \ \ \ \ ext { (Dog not evaluate.) }\end{array} $$

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Use common logarithms or natural logarithms and a calculator to evaluate the expression. $$ \begin{array}{l}\log _{18} 19 \ 	ext { Use the change-of-base property to rewrite the given } \ 	ext { expression in terms of natural logarithms or common } \ \operatorname{logarithms.~} \ \ \ \ 	ext { (Dog not evaluate.) }\end{array} $$

UpStudy AI · Accepted Answer

Let the expression be 
$$
\log_{18} 19.
$$

We use the change-of-base formula, which states that
$$
\log_b a = \frac{\log_c a}{\log_c b}
$$
for any positive value $$ c $$ (commonly $$ c = 10 $$ or $$ c = e $$).

Using natural logarithms $$ (\ln) $$, we rewrite the expression as
$$
\log_{18} 19 = \frac{\ln 19}{\ln 18}.
$$

Alternatively, using common logarithms $$ (\log) $$, we have
$$
\log_{18} 19 = \frac{\log 19}{\log 18}.
$$

These are the required forms using the change-of-base property.
Use the change-of-base formula to rewrite $$ \log_{18} 19 $$ as $$ \frac{\ln 19}{\ln 18} $$ or $$ \frac{\log 19}{\log 18} $$.

Use common logarithms or natural logarithms and a
calculator to evaluate the expression.

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