$27^x+3^{x+1} = 100$. Find an exact solution in terms of logarithms.
I've tried this in many different ways and can't find any leeway. I also can not find anything to help me online.
2026-05-16 13:05:04.1778936704
$27^x+3^{x+1} = 100$. Find an exact solution in terms of logarithms.
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Hint: Let $y=3^x$ and get a cubic equation for $y$. Then $x = \log_3 y$.