#### Answer

$x\approx2.810$

#### Work Step by Step

Using the properties of equality, the given equation, $
4.9^x-87=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
4.9^x=87
.\end{array}
Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the equation, $
4.9^x=87
,$ is
\begin{array}{l}\require{cancel}
\ln4.9^x=\ln87
\\\\
x\ln4.9=\ln87
\\\\
x=\dfrac{\ln87}{\ln4.9}
\\\\
x\approx2.810
.\end{array}