Final answer to the problem
$\log_{5}\left(5^{\frac{3}{2}}\right)$
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Step-by-step Solution
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- Prime Factor Decomposition
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1
The product of powers of the same base is equal to the base raised to the sum of the exponents: $a^m\cdot a^n=a^{m+n}$
Learn how to solve properties of logarithms problems step by step online.
$\log_{5}\left(5^{\left(\frac{1}{2}+1\right)}\right)$
Learn how to solve properties of logarithms problems step by step online. Simplify log5(5*5^(1/2)) applying logarithm properties. The product of powers of the same base is equal to the base raised to the sum of the exponents: a^m\cdot a^n=a^{m+n}. Simplify the addition \frac{1}{2}+1. Multiply 1 times 2. Add the values 1 and 2.
Final answer to the problem
$\log_{5}\left(5^{\frac{3}{2}}\right)$
Exact Numeric Answer
$1.5$
