Change the left side to \(\displaystyle 6^2\) and the right side to \(\displaystyle 6^{-1}\) so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other (\(\displaystyle 20x+4=-13+x\)). \(\displaystyle x=-\frac{17}{19}\).

Change the left side to \(\displaystyle 2^3\) and the right side to \(\displaystyle 2^{-4}\) so that both sides have the same base. Apply log and then set the exponential expressions equal to each other (\(\displaystyle 3x-3=-16x+12\)). Thus, \(\displaystyle x=\frac{15}{19}\).

Change the left side to \(\displaystyle 5^2\) and the right side to \(\displaystyle 5^{-3}\) so that both sides have the same base. Apply log and then set the exponential expressions equal to each other (\(\displaystyle 40x+8=-12+9x\)). Thus, \(\displaystyle x=-\frac{20}{31}\)

Change the left side to \(\displaystyle 3^3\) and the right side to \(\displaystyle 3^{-1}\) so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other (\(\displaystyle 12x-3=-3x-8\)). Thus, \(\displaystyle x=-\frac{1}{3}\).

\(\displaystyle log_{10}10000\) can be simplified to \(\displaystyle 4\) since \(\displaystyle 10^4 = 10000\). This gives the equation:

\(\displaystyle 17 + x = 4\)

Subtracting \(\displaystyle 17\) from both sides of the equation gives the value for \(\displaystyle x\).

\(\displaystyle (17 + x) - 17 = (4) - 17 \rightarrow x = -13\)

First, change 25 to \(\displaystyle 5^2\) so that both sides have the same base. Once they have the same base, you can apply log to both sides so that you can set their exponents equal to each other, which yields \(\displaystyle 3x-9=2x+10\).

\(\displaystyle x=19\)

Change 49 to \(\displaystyle 7^2\) so that both sides have the same base so that you can apply log. Then, you can set the exponential expressions equal to each other \(\displaystyle 3x+4=2x+2\).

Thus, \(\displaystyle x=-2\)

Change the right side to \(\displaystyle 10^{-2}\) so that both sides have the same bsae of 10. Apply log and then set the exponential expressions equal to each other

\(\displaystyle 2x-10=-16x+2\)

Change 64 to \(\displaystyle 4^3\) so that both sides have the same base. Apply log to both sides so that you can set the exponential expressions equal to each other

\(\displaystyle 2x-7=9x\).

Thus, \(\displaystyle x=-1\).

Change 125 to \(\displaystyle 5^3\) so that both sides have the same base. Apply log and then set the exponential expressions equal to each other so that \(\displaystyle 11-3x=15-3x\). Upon trying to isolate \(\displaystyle x\), it becomes clear that there is no solution.