Given the exponential function:
[tex]10^{2a+3}=10^{a-4}[/tex]Let's evaluate the given exponential function.
Since the base of both sides are the same, the expressions are equal if the exponents are equal.
Remove the bases and equate the exponents:
[tex]2a+3=a-4[/tex]Subtract 3 from both sides:
[tex]\begin{gathered} 2a+3-3=a-4-3 \\ \\ 2a=a-7 \end{gathered}[/tex]Subtract a from both sides:
[tex]\begin{gathered} 2a-a=a-a-7 \\ \\ a=-7 \end{gathered}[/tex]ANSWER:
a = -7
