Solve 6^x+2 = 10 for x using the change of base formula

asked Nov 19, 2023 54.2k views

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Answer:

$x\approx-0.7149$

Explanation:

$\displaystyle 6^(x+2)=10\\\\\log_6(6^(x+2))=\log_6(10)\\\\x+2=(\log(10))/(\log(6))\\\\x+2\approx1.2851\\\\x\approx-0.7149$

Recall that the change of base formula is
$\displaystyle \log_a(b)=(\log(b))/(\log(a))$

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