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h) i) Solve for x in 27^x = 93x−2

April 27, 2026Mathematics

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Step-by-step solution

4 steps

$27^x = 9^{3x-2}$

Solve for $x$ in

Express both bases as powers of the same number, 3.
$(3^3)^x = (3^2)^{3x-2}$
Apply the power rule $(a^m)^n = a^{mn}$ .
$3^{3x} = 3^{2(3x-2)}$ $3^{3x} = 3^{6x-4}$
Equate the exponents since the bases are the same.
$3x = 6x-4$
Solve for $x$ .
$3x - 6x = -4$ $-3x = -4$ $x = \frac{-4}{-3}$ $x = \frac{4}{3}$
The solution for h) i) is $\boxed{x =

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