(i) #10; #10; 4^2x #10;= 132 #10; #10; ( #10;2^2)^2x = 125 #10; #10; 2^4x #10;= 2^ 5 #10; #10; 4x #10;= #160; 5 ...

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Laws of Exponents for Real Numbers

Find x if ...

Question

Find $x$ if $4^{2 x} = \frac{1}{32}$

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Solution

(i)

$4^{2 x} = \frac{1}{32}$

${(2^{2})}^{2 x} = \frac{1}{25}$

$2^{4 x} = 2^{- 5}$

$4 x = - 5$

$x = \frac{- 5}{4}$

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