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Solve for y in terms of x using logarithm properties: 3 y = x 3 2 + 3 6

April 19, 2026Mathematics

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Answer

y = 6 \cdot 2^x

4 steps

Apply the power rule of logarithms, $c \log_b M = \log_b (M^c)$ , to the term $x \log_3 2$ .
$x \log_3 2 = \log_3 (2^x)$
Substitute this back into the original equation.
$\log_3 y = \log_3 (2^x) + \log_3 6$
Apply the product rule of logarithms, $\log_b M + \log_b N = \log_b (MN)$ , to the right side of the equation.
$\log_3 y = \log_3 (2^x \times 6)$ $\log_3 y = \log_3 (6 \cdot 2^x)$
Since the logarithms on both sides have the same base, we can equate their arguments.
$y = 6 \cdot 2^x$

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