Final answer to the problem
$x=\frac{\log_{2}\left(\frac{1}{1048576}\right)-18}{-12}$
Got another answer? Verify it here!
Step-by-step Solution
Learn how to solve exponential equations problems step by step online. Solve the exponential equation 4^(9-6x)=(1/64)^(10/3). The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Decompose 4 in it's prime factors. Simplify \left(2^{2}\right)^{\left(9-6x\right)} 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 9-6x. We can take out the unknown from the exponent by applying logarithms in base 10 to both sides of the equation.
Final answer to the problem
$x=\frac{\log_{2}\left(\frac{1}{1048576}\right)-18}{-12}$
Exact Numeric Answer
$x=3.1666667$
