Final answer to the problem
$x=\frac{3}{10}$
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Step-by-step Solution
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1
Decompose $8$ in it's prime factors
$2^x\left(2^{3}\right)^{\left(5x-1\right)}=64^x$
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$2^x\left(2^{3}\right)^{\left(5x-1\right)}=64^x$
Learn how to solve exponential equations problems step by step online. Solve the exponential equation 2^x8^(5x-1)=64^x. Decompose 8 in it's prime factors. Simplify \left(2^{3}\right)^{\left(5x-1\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals 5x-1. Apply the exponent property of product of powers: x^a\cdot x^b=x^{a+b}. Rewrite the power 64^x with base 2.
Final answer to the problem
$x=\frac{3}{10}$
Exact Numeric Answer
$x=0.3$