# logs past paper question

• Jan 8th 2012, 10:46 AM
mathkid12
logs past paper question
log2 x = log 4x +6
this is a question my teacher gave us, the she gave this the first equation on starting the question which is below

log2x = log2x +6 / log24

how did my teacher got this, i need to know because i am presently studing for an exam

PS the 2 and 4 is subscrip SORRY AND final log24 only the 2 is subscript
• Jan 8th 2012, 11:08 AM
earboth
Re: logs past paper question
Quote:

Originally Posted by mathkid12
log2 x = log 4x +6
this is a question my teacher gave us, the she gave this the first equation on starting the question which is below

log2x = log2x +6 / log24

how did my teacher got this, i need to know because i am presently studing for an exam

PS the 2 and 4 is subscrip SORRY AND final log24 only the 2 is subscript

1. You can convert logs of a certain base into logs of another base by using:

$\log_a(b)=\frac{\log_c(b)}{\log_c(a)}$

2. Re-write the given equation:

$\log_2(x)=\log_4(x)+6~\implies~ \\ \log_2(x)=\frac{\log_2(x)}{\log_2(4)}+6~\implies~ \\ \log_2(x)=\frac{\log_2(x)}{2}+6$

3. Collect like terms:

$\frac12 \log_2(x)=6~\implies~\log_2(x)=12~\implies~x=2^{12 }=4096$