Final Answer
$\log_{3}\left(17\right)+1+\log_{3}\left(2\right)\left(-1\right)+\log_{3}\left(5\right)\left(-1\right)$
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Step-by-step Solution
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The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$
$\log_{3}\left(51\right)-\log_{3}\left(10\right)$
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$\log_{3}\left(51\right)-\log_{3}\left(10\right)$
Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression log3((51/10)). The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Decompose 51 in it's prime factors. Decompose 10 in it's prime factors. Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=17 and N=3.
Final Answer
$\log_{3}\left(17\right)+1+\log_{3}\left(2\right)\left(-1\right)+\log_{3}\left(5\right)\left(-1\right)$
Exact Numeric Answer
$1.483$