Final answer to the problem
$x=\frac{2\log_{4}\left(\frac{1}{64}\right)+10}{1-5\log_{4}\left(\frac{1}{64}\right)}$
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Step-by-step Solution
Learn how to solve problems step by step online. Solve the exponential equation 4^(x-10)=(1/64)^(5x+2). We can take out the unknown from the exponent by applying logarithms in base 10 to both sides of the equation. Use the following rule for logarithms: \log_b(b^k)=k. We need to isolate the dependent variable x, we can do that by simultaneously subtracting -10 from both sides of the equation. Canceling terms on both sides.
Final answer to the problem
$x=\frac{2\log_{4}\left(\frac{1}{64}\right)+10}{1-5\log_{4}\left(\frac{1}{64}\right)}$
Exact Numeric Answer
$x=0.25$
