Question

Rewrite the expression as an equivalent ratio of logs using the indicated base.log17(52.875) to base 10.

Answer 1

Answer:

$log_{17}52.875 = log_{10}52.875 : log_{10}17}$

Step-by-step explanation:

Given

$log_{17}(52.875)$

Required

Convert to base 10

To do this, we make use of the following logarithm laws;

$log_ba = \frac{log_{10}a}{log_{10}b}$

In the given parameters;

$a = 52.875$

$b = 17$

Substitute these values in $log_ba = \frac{log_{10}a}{log_{10}b}$

$log_{17}52.875 = \frac{log_{10}52.875}{log_{10}17}$

Represent as a ratio

$log_{17}52.875 = log_{10}52.875 : log_{10}17}$

Hence;

$log_{17}(52.875)$ is represented as $log_{17}52.875 = log_{10}52.875 : log_{10}17}$

Answer 2

Expression  $log_{17} 52.875$ can be written as in form of ratio of log  $\frac{log_{10} 52.875}{log_{10} 17}$ .

Any logarithmic expression $log_{a} b$ can we written as in form of ratio of log on base 10.

                   $log_{a} b=\frac{log_{10} b}{log_{10} a}$

Here logarithmic expression is,  $log_{17} 52.875$ comparing with above expression.

We get,    $b=52.875,a=17$

Substitute values of a and b in above expression.

 We get,      $log_{17} 52.875=\frac{log_{10} 52.875}{log_{10} 17}$

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