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I am trying to find the point where $y=5$ intersects the curve $$y=1+3^x$$ My working so far: $$5=1+3^x$$

$$4=3^x$$

How do I work out this last step accurately?

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2 Answers 2

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$$ 4 = 3^x \implies \log 4 = x \log 3 \implies x = \color{red}{\frac{\log 4}{\log 3}}$$

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Take the logarithm. It holds: $log_b(a^x) = x log_b (a)$ for any number $a$ and any Kind of logarithm to Basis $b$.

Hint: Use the logarithm to Basis 3.

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