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Exercise

$3^{5x}=27^{2x+1}$

Step-by-step Solution

Learn how to solve problems step by step online. Solve the exponential equation 3^(5x)=27^(2x+1). Rewrite the power 27^{\left(2x+1\right)} with base 3. Simplify \left(3^{3}\right)^{\left(2x+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 2x+1. If the bases are the same, then the exponents must be equal to each other. Solve the product 3\left(2x+1\right).
Solve the exponential equation 3^(5x)=27^(2x+1)

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Final answer to the exercise

$x=-3$

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