Question

Use logarithms to solve each equation 2x9/8=111

Answer 1

We have this equation:


`2x^{(9)/(8)} = 111`

and we need to find the value of x.

First of all, we multiply the whole equation for 1/2, so our goal is to isolate x, therefore:


`x^{(9)/(8)}=(111)/(2)`

Next step we must do is to apply logarithms:


`logx^{(9)/(8)} = log((111)/(2))`

Next, we have to apply identities and then to solve the equation:


`(9)/(8)logx = log((111)/(2))`

`logx = (8)/(9)log((111)/(2))`

`logx = 1.5504`

`10^(logx) = 10^(1.5504)`

Finally, we have the value of x which was our goal. This is the answer for the question above:


`x= 35.5140`