Question

Please show your work for this question

Answer 1

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$4 \times {9}^{2x} = 42$

Divide sides by 4

$\frac{4 \times {9}^{2x} }{4} = \frac{42}{4}$

${9}^{2x} = \frac{2 \times 21}{2 \times 2}$

${9}^{2x} = \frac{21}{2}$

$( { {9}^{2} })^{x} = \frac{21}{2}$

$x = log_{ {9}^{2} }( \frac{21}{2} )$

$x = \frac{1}{2} log_{9}( \frac{21}{2} )$

$x = \frac{1}{2} log_{ {3}^{2} }( \frac{21}{2} )$

$x = \frac{1}{2 \times 2} log_{3}( \frac{21}{2} )$

$x = \frac{1}{4} log_{3}( \frac{21}{2} )$

$x = \frac{1}{4} ( \: \: log_{3}(21) - log_{3}(2) \: \: )$

$x = \frac{1}{4} ( \: \: log_{3}(3 \times 7) - log_{3}(2) \: \: )$

$x = \frac{1}{4} ( \: \: log_{3}(3) + log_{3}(7) - log_{3}(2) \: \: )$

$x = \frac{1}{4} ( \: \: 1 + log_{3}(7) - log_{3}(2) \: \: )$

And we're done...

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