Evaluate $log_5(10)xxlog_5(x)=log_5(100)$ ?

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Answer 1 · 2017-03-29T03:25:48

$x=25$

We have:

$log_5(10)xxlog_5(x)=log_5(100)$

$log_5x=log_5(100)/log_5(10)=((log100)/log5)/(log10/log5)=log100/log5xxlog5/log10=log100/log10=2/1=2$

We can now rewrite the log as an exponential, following the form:

$log_a(b)=c=>a^c=b$

$log_5(x)=2=>5^2=x=25$

Answer 2 · 2017-03-29T04:54:18

$x = 25$

$log_5 10 * log_5 x = log_5 100$

$log_5 x = log_5 100/log_5 10$

$log_5 x = log_5 100/log_5 10 = (log_10 100/log_10 5) / (log_10 10/log_10 5)$ -> change it base from 5 to 10.

$log_5 x = log_10 100 / log_10 10 = 2$

$log_5 x= 2$

$x = 5^2 =25$

Evaluate log_5(10)xxlog_5(x)=log_5(100)log_5(10)xxlog_5(x)=log_5(100)?