How to solve and check: log x^2 - log 8 = log 8

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve : log x^2 - log 8 = log 8

log x^2 - log 8 = log 8

use the property of logarithm : log a^b = b*log a and log a + log b = log a*b

=> 2*log x = 2*log 8

=> log x = log 8

=> x = 8

To check the result you can find the values of log 64 and log 8. You will see that log 64 - log 8 = log 8.

The solution of log x^2 - log 8 = log 8 is x = 8.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

log x^2 - log 8 = log 8

First we will add log 8 to both sides.

==> log x^2 = log 8 + log 8

==> log x^2 = 2*log 8

But we know that a*log b = log b^a

==> 2*log 8 = log 8^2

==> log x^2 = log 8^2

Since the log are equal then x^2 = 8^2

==> x = 8

To check we will substitute :

log 8^2 - log 8 = log 8

==> 2log 8 - log 8 = log 8

==> log 8 = log 8

Then the answer is x = 8

 

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