How do you solve $5*11^(5a+10)=57$ ?

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Answer 1 · 2016-10-16T02:46:36

$a=-1.797$

$5 * 11^(5a+10)=57$

$(5*11^(5a+10))/5=57/5color(white)(aaa)$ Divide both sides by 5

$11^(5a+10)=57/5$

$log(11^(5a+10))=log (57/5)color(white)(aaa)$ Take the log of both sides

$(5a+10)log11=log(57/5)color(white)(aa)$ Use the log rule $logx^a=alogx$

$frac{(5a+10)log11}{log11}=frac{log(57/5)}{log11}color(white)(aa)$ Divide both sides by log11

$5a+10=frac{log(57/5)}{log11}$

$color(white)(aa)-10color(white)(aaa)-10color(white)(aaa)$ Subtract 10 from both sides

$5a=frac{log(57/5)}{log11}-10$

$(5a)/5=frac{frac{log(57/5)}{log11}-10}{5}color(white)(aaa)$ Divide both sides by 5

$a=-1.797color(white)(aaa)$ Use a calculator

How do you solve 5*11^(5a+10)=575*11^(5a+10)=57?