Use the change of base property to rewrite the given expression in terms of natural logarithm or common logarithm

Question

asked Mar 16, 2023 179k views

1 Answer

Jungy · Answer 1 · 2023-03-22T05:28:10+0000

ANSWER

$\begin{gathered} \frac{\operatorname{\log}_(10)17.3}{\operatorname{\log}_(10)0.2} \\ -1.7712 \end{gathered}$

Step-by-step explanation

To rewrite the given logarithm in terms of a common logarithm, apply the following law of logarithm to rewrite it in terms of base 10:

$\log_ab=(\log_(10)b)/(\log_(10)a)$

Therefore, the given logarithm becomes:

$(\log_(10)17.3)/(\log_(10)0.2)$

To evaluate the expression, use a calculator or logarithm table to find the value of the logarithms and simplify:

$\begin{gathered} (1.2380)/(-0.6990) \\ -1.7712 \end{gathered}$

That is the answer.