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Solve the equation 6^X = X18 for X.

April 23, 2026Mathematics

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Step-by-step solution

4 steps

Write the given equation.
$6^X = X^{18}$
Take the $1/(18X)$ power of both sides of the equation.
$(6^X)^{\frac{1}{18X}} = (X^{18})^{\frac{1}{18X}}$
Simplify the exponents using the rule $(a^b)^c = a^{bc}$ .
$6^{\frac{X}{18X}} = X^{\frac{18}{18X}}$ $6^{\frac{1}{18}} = X^{\frac{1}{X}}$
We are looking for a value of $X$ that satisfies $X^{\frac{1

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