Question

what is the value of x in this logarithmic equation?
`(1)/(g^(5)) = (g^{ (9)/(5)})^(x)`

Answer 1

`(1)/(g^5)=(g^{(9)/(5)})^x`

This can be re-written as;

`g^(-5)=g^{(9x)/(5)}`

we can now equate the powers

`-5\text{ =}(9x)/(5)`

Multiply both-side of the equation by 5/9

-5(5/9) = x

-25/9 = x

`x=-2(7)/(9)`

or

x= -2.78