Question

Solve. 90$x$ = 27.

Answer 1

Answer: $x$≈$0.732$

Step-by-step explanation:

You need to find the value of the variable "x".

To solve for "x" you need to apply the following property of logarithms:

$log(m)^n=nlog(m)$

Apply logarithm on both sides of the equation:

$90^x=27\\\\log(90)^x=log(27)$

Now, applying the property mentioned before, you can rewrite the equation in this form:

$xlog(90)=log(27)$

Finally, you can apply the Division property of equality, which states that:  

 $If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}$

Therefore, you need to divide both sides of the equation by $log(90)$. Finally, you get:

$\frac{xlog(90)}{log(90)}=\frac{log(27)}{log(90)}\\\\x=\frac{log(27)}{log(90)}$

$x$≈$0.732$