The value of x will be equal to 2.477.
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;-
[tex]5^{x-2}= 8[/tex]
Taking Log on both sides.
[tex]Log_e 5^{x-2}=Log_e8[/tex]
(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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