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Property 4

Find x, if : ...

Question

Find x, if :

$x - l o g 48 + 3 l o g 2 = \frac{1}{3} l o g 125 - l o g 3$

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Solution

$c o n s i d e r space t h e space e q u a t i o n x minus log 48 plus 3 log 2 equals 1 third log 125 minus log 3 rightwards double arrow x equals 1 third log 125 minus log 3 plus log 48 minus 3 log 2 rightwards double arrow x equals log open parentheses 125 close parentheses to the power of 1 third end exponent minus log 3 plus log 48 minus log 2 cubed rightwards double arrow x equals log open parentheses 5 cubed close parentheses to the power of 1 third end exponent minus log 3 plus log 48 minus log 8 rightwards double arrow x equals log 5 plus log 48 minus log 3 minus log 8 rightwards double arrow x equals log open parentheses 5 cross times 48 close parentheses minus log space open parentheses 3 cross times 8 close parentheses rightwards double arrow x equals log fraction numerator 5 cross times 48 over denominator 3 cross times 8 end fraction rightwards double arrow x equals log 10 rightwards double arrow x equals 1 rightwards double arrow x equals$

So the value of x =1.

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