How do you solve $4^{x} = 3$ $4^x=3$ ?

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How do you solve $4^{x} = 3$ $4^x=3$ ?

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Answer 1 · 2016-05-06T17:43:00

The first thing we should realise is that 3 is not a power of 4, so this will have to be solved by logs. $4^{1} = 4$ $4^1 = 4$ , so $x < 1$ $x<1$
$x = 0.792$ $x = 0.792$

Explanation:

$4^{x} = 3$ $4^x = 3$

${log 4}^{x} = log 3$ $log4^x = log3$
$x log 4 = log 3$ $x log 4 =log 3$

$x = \frac{log 3}{log 4}$ $x = (log3)/(log4)$

There are no log laws to simplify this, it has to be done on a calculator: $x = 0.792$ $x = 0.792$

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How do you solve $4^{x} = 3$ $4^x=3$ ?

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