Solving a logarithmic equation. I need help on solving them when they are in exponents. x

osmane5e

osmane5e

Answered question

2022-05-23

Solving a logarithmic equation. I need help on solving them when they are in exponents.
x 2 log 3 x 3 / 2 log x = 10
Can someone help me to solve it?
Also, when we have 2 log 2 x, is it equal to 4 ( log x ) 2

Answer & Explanation

morssiden5g

morssiden5g

Beginner2022-05-24Added 9 answers

Assuming that with log you mean the decimal logarithm, your equation is equivalent to
log ( x t ) = log 10
where t = 2 ( log x ) 3 3 2 log x, so to
t log x = 1 2 .
Note that I wrote the clearer ( log x ) 3 rather than the ambiguous log 3 x, but it's just a matter of conventions.
Now, set y = log x and rewrite your equation by substituting t = 2 y 3 3 2 y:
( 2 y 3 3 2 y ) y = 1 2
which shouldn't be too difficult to solve (it's a biquadratic).
Aidyn Cox

Aidyn Cox

Beginner2022-05-25Added 5 answers

Regarding your question:
2 log 3 x = 2 ( log x ) 3 4 ( log x ) 2
If we had 2 log ( x 3 ) , then
2 log ( x 3 ) = log ( ( x 3 ) 2 ) = log ( x 6 )

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