Prove the logarithmic identity

[Math Tutor]

Prove the logarithmic identity:
[tex]log_312 = log_37 \times log_75 \times log_54 + 1[/tex]

[idontknow]

And this is a problem ...
I don't know LaTeX but!
log 7 base 3 = 1 / log 3 base 7

log 5 base 7 / log 3 base 7 = log 5 base 3= 1 / log 3 base 5

log 4 base 5 / log 5 base 3 = log 4 base 3
log 4 base 3 + 1 =log 12 base 3
log 4 base 3 + log 3 base 3 = log 12 base 3

[Guest]

[tex]log_{3 } 12-log_{3 } 7 .log_{7 } 5 .log_{5 } 4[/tex] = 1

[tex]log_{3 }[/tex]12 -[tex]\frac{lg7}{lg3} .\frac{lg5}{lg7} .\frac{lg4}{lg5}[/tex] =

=[tex]log_{3 }[/tex]12 -[tex]\frac{lg4}{lg3}[/tex]=

=[tex]log_{3 }12 - log_{3 }4[/tex] =

= [tex]log_{3 } \frac{12}{4}[/tex]=

=[tex]log_{3 }[/tex]3 = 1