common logarithms: solve logX/log81 =log3/logX

[padamarthur]

solve logX/log81 =log3/logX

my solution is; log(logX/log81)=log(log3/logX)

or
my solution is; (logX)(logX)=(log81)(log3)

PS I'm new any advice on how to structure my question like fractions without using a forward slash?

 

[Deleted member 4993]

solve logX/log81 =log3/logX

my solution is; log(logX/log81)=log(log3/logX)

or
my solution is; (logX)(logX)=(log81)(log3)

PS I'm new any advice on how to structure my question like fractions without using a forward slash?

Convert all the log to log₃ (base 3 log).

 

[pka]

solve logX/log81 =log3/logX

Can you prove \(\displaystyle \large \log(81)\cdot\log(3)=4[\log(3)]^2~? \)

 

[padamarthur]

log(81)log(3)
log(3⁴)log(3)
4log(3)log(3)
therfore=4log(3)²

 

[stapel]

log(81)log(3)
log(3⁴)log(3)
4log(3)log(3)
therfore=4log(3)²

Okay; now, can you relate this to the original equation?