Answer
$x\approx4.50$
Work Step by Step
Most exponential equations cannot be rewritten so that each side has the same base. To solve those kind of exponential equation, the solutions begins with isolating the exponential expression. Then, we take the logarithm on both sides. All logarithmic relations are function. Thus, if $M$ and $N$ are positive real numbers and $M=N,$ then $\log_{b}M=\log_{b}N.$ The base that can be used when taking logarithm on both sides of an equation can be any base at all. Thus, using logarithm to solve exponential equations,
1. Isolate the exponential expression
2. Take the common logarithm on both sides of the equation for base $10$. Take the natural logarithm on both sides of the equation for bases other than $10.$
3. Simplify using one of the following properties:
$\ln b^x=x\ln b$ or $\ln e^x=x,$ or $\log 10^x=x$
4. Solve for the variable,
eg, $3^x=140$
$x\ln 3=\ln 140,$
$x=\frac{\ln 140}{\ln 3}\approx4.50$
