Solving this logarithm equation? How do I solve this equation using

Janessa Olson 2022-07-05 Answered
Solving this logarithm equation?
How do I solve this equation using common logarithms?
log x = 1 log ( x 3 )
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Answers (2)

Mekjulleymg
Answered 2022-07-06 Author has 14 answers
Hint:
1 = log x + log ( x 3 ) 1 = log ( x ( x 3 ) )
Now use an exponent to remove the logarithm.

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Janet Forbes
Answered 2022-07-07 Author has 4 answers
Let 1 = log 10 then,
log x = log 10 log ( x 3 ) .
For all x and y and a constant a, one always has
(1) log a x y = log a x + log a y .
This is one of the most important logarithm rules. From this rule, we can express log x y
log x y = log x ( 1 y ) ,
and from (1), we see that
log x y = log x + log 1 y = log x + log y 1 .
10 d = y 1 1 10 d = 1 y 1 10 d = y
log y = d log y = d .
Since we asserted that d = log y 1 then
log x y = log x log y .
Do you notice how useful the rule (1) is? This implies that
log x = log 10 log ( x 3 )   x 2 3 x 10 = 0.
We can solve for x in this trinomial using the quadratic formula, such that
x = 3 ± 7 2 x = 2    or    x = 5.
If you are not familiar with the quadratic formula, comment below.

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