Question

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

Answer 1

We have this equation:

$2x^{\frac{9}{8}} = 111$

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:

$x^{\frac{9}{8}}=\frac{111}{2}$
 
Next step we must do is to apply logarithms:

$logx^{\frac{9}{8}} = log(\frac{111}{2})$

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

$\frac{9}{8}logx = log(\frac{111}{2})$
$logx = \frac{8}{9}log(\frac{111}{2})$
$logx = 1.5504$
$10^{logx} = 10^{1.5504}$

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

$x= 35.5140$