Final Answer
$x=\frac{\log_{2}\left(\frac{1}{16}\right)}{2}$
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Step-by-step Solution
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1
Decompose $4$ in it's prime factors
$\left(2^{2}\right)^x=\frac{1}{16}$
Learn how to solve definition of derivative problems step by step online.
$\left(2^{2}\right)^x=\frac{1}{16}$
Learn how to solve definition of derivative problems step by step online. Solve the exponential equation 4^x=1/16. Decompose 4 in it's prime factors. Simplify \left(2^{2}\right)^x using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals x. 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.
Final Answer
$x=\frac{\log_{2}\left(\frac{1}{16}\right)}{2}$
Exact Numeric Answer
$x=-2$