Answer
$x \approx 2.45$
Work Step by Step
Add 2 to both sides of the equation to obtain
$e^{5x-3}-2+2=10476+2
\\e^{5x-3}=10478.$
The base in the exponential equation is $e$ so take the natural logarithm on both sides to obtain
$\ln{e^{5x-3}}=\ln{10478}.$
Use the property $\ln{e^b}=b$ (where b=5x-3) on the left side to obtain
$5x-3 = \ln{10478}.$
Solve for $x$:
$5x-3+3 = \ln{10478}+3
\\5x=\ln{10478} +3
\\x=\dfrac{\ln{10478}+3}{5}.$
Use a calculator and round-off the answer to two decimal places to obtain
$x \approx 2.45.$
