Please show your work for this question

Question

asked May 3, 2021 93.1k views

1 Answer

JustLearn · Answer 1 · 2021-05-10T05:46:32+0000

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

$4 * {9}^(2x) = 42$

Divide sides by 4

$\frac{4 * {9}^(2x) }{4} = (42)/(4) \\$

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

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

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

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

$x = (1)/(2) log_(9)( (21)/(2) ) \\$

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

$x = (1)/(2 * 2) log_(3)( (21)/(2) ) \\$

$x = (1)/(4) log_(3)( (21)/(2) ) \\$

$x = (1)/(4) ( \: \: log_(3)(21) - log_(3)(2) \: \: ) \\$

$x = (1)/(4) ( \: \: log_(3)(3 * 7) - log_(3)(2) \: \: ) \\$

$x = (1)/(4) ( \: \: log_(3)(3) + log_(3)(7) - log_(3)(2) \: \: ) \\$

$x = (1)/(4) ( \: \: 1 + log_(3)(7) - log_(3)(2) \: \: ) \\$

And we're done...

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️