How do you solve $log 516 - log 52 t = log 52$ $log516 - log52t = log52$ ?

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How do you solve $log 516 - log 52 t = log 52$ $log516 - log52t = log52$ ?

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Answer 1 · 2015-11-15T04:51:14

Remember the logarithm rule: ${log}_{a} (\frac{x}{y}) = {log}_{a} x - {log}_{a} y$ $log_(a)(x/y)=log_ax-log_ay$
You can work in reverse:
$log 516 - log 52 t = log 52$ $log516-log52t=log52$
$log (\frac{516}{52 t}) = log 52$ $log(516/(52t))=log52$

Now, there are multiple things you could do from here, but the easiest would be to recognize that if $log a = log b, a = b$ $loga=logb,a=b$ .
Therefore, $\frac{516}{52 t} = 52$ $516/(52t)=52$ .
We can solve for $t$ $t$ .
$516 = 2704 t^{2}$ $516=2704t^2$
$\frac{516}{2704} = t^{2}$ $516/2704=t^2$
$\sqrt{\frac{516}{2704}} = t$ $sqrt(516/2704)=t$
$\sqrt{\frac{129}{676}} = t$ $sqrt(129/676)=t$

Notice that we only use the positive square root, excluding $- \sqrt{\frac{129}{676}}$ $-sqrt(129/676)$ . We must do this since if we plugged $- \sqrt{\frac{129}{676}}$ $-sqrt(129/676)$ into $log 52 t$ $log52t$ , we would get a negative number, which is impossible.

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How do you solve $log 516 - log 52 t = log 52$ $log516 - log52t = log52$ ?

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How do you solve $log 516 - log 52 t = log 52$ $log516 - log52t = log52$ ?