Question

What is the approximate value of x in the equation below? log Subscript 5 Baseline 15 = x 3.

Answer 1

The approximate value of x in the equation using change of the base of logarithmic rule found as -1.317.

What is change of base rule of logarithmic function?

The change of base rule of the log is used to write the given logarithmic number in terms of ratio of two log numbers.

For example,

$\log_ba=\dfrac{\log_xa}{\log_xb}$

Here, a,b is the real number and x is the base.

The logarithmic equation given in the problem is,

$log_5(15) = x+ 3$

Using the change of base formula, the above equation can be written as,

$\dfrac{log{15} }{log{5} }= x+ 3$

Isolate the x variable as,

$x=\dfrac{log{15} }{log{5} }- 3\\x=\dfrac{1.17609}{0.69897}- 3\\x\cong-1.317$

Hence, the approximate value of x in the equation using change of the base of logarithmic rule found as -1.317.

Learn more about the rules of logarithmic function here;

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