Mathematics: Please show your work for this question

Please show your work for this question

chloebaby8

10.02.2022

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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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oldless504

14.12.2021

C) -1/4x+2=2x-7

Step-by-step explanation:

-1/4(4)+2=2(4)-7

-1+2=8-7

1=1

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