Question

Explain how to solve 5^(x-2)=8 using log base b of y equals log y over log b. include the solution for x in your answer. round your answer to the nearest thousandth.

Answer 1

The value of x will be equal to 2.477.

What is a logarithm?

The logarithm is the inverse function of exponentiation in mathematics. That is, the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised in order to obtain that number x.

The given expression will be solved as follows;-

$5^{x-2}= 8$

Taking Log on both sides.

$Log_e 5^{x-2}=Log_e8$

(x-2) Log5 = Log 8

( x-2) = Log8 / Log 5

(x - 2) = Log 8 - Log 5

(x - 2 ) = Log 3

x-2 = 0.477

x  =  2.477

Therefore the value of x will be equal to 2.477.

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