Solve 1/2log 25 - 2log3 + 2 log 6

April 14, 2026Mathematics

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Answer

\mathbf{\log 20}

6 steps

Apply the power rule of logarithms, $a \log b = \log b^a$ , to each term.
$\frac{1}{2}\log 25 = \log 25^{1/2} = \log \sqrt{25} = \log 5$ $2\log 3 = \log 3^2 = \log 9$ $2\log 6 = \log 6^2 = \log 36$
Substitute these simplified terms back into the original expression.
$\log 5 - \log 9 + \log 36$
Apply the subtraction rule of logarithms, $\log a - \log b = \log \left(\frac{a}{b}\right)$ .
$\log 5 - \log 9 = \log \left(\frac{5}{9}\right)$
Apply the addition rule of logarithms, $\log a + \log b = \log (a \cdot b)$ .
$\log \left(\frac{5}{9}\right) + \log 36 = \log \left(\frac{5}{9} \times 36\right)$
Simplify the expression inside the logarithm.
$\frac{5}{9} \times 36 = 5 \times \frac{36}{9} = 5 \times 4 = 20$
Write the final simplified expression.
$\log 20$

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