# Thread: logarithmic equation

1. ## logarithmic equation

Solve the logarithmic equation

Log(sub 9)x = 3/2

I have the equation as far as

Log 9*3/2 = x

but I am unsure if this is correct or not. Please help? Thanks!

2. Originally Posted by Deathscyth3
Solve the logarithmic equation

Log(sub 9)x = 3/2

I have the equation as far as

Log 9*3/2 = x

but I am unsure if this is correct or not. Please help? Thanks!
$\displaystyle \log_a b \Longleftrightarrow \frac {log_c b}{log_c a}$

$\displaystyle \log_9 x = \frac {3}{2}$

$\displaystyle \log_9 x = \frac {logx}{log9}$

$\displaystyle \frac {logx}{log9} = \frac {3}{2}$

Solve for x. Please note that logarithms should be part of the Algebrea/Pre-Algebra category, and not pre-calculus.

3. Originally Posted by Deathscyth3
Solve the logarithmic equation

Log(sub 9)x = 3/2

I have the equation as far as

Log 9*3/2 = x

but I am unsure if this is correct or not. Please help? Thanks!
Remember that

$\displaystyle log_a(b)=c \iff a^c=b$

$\displaystyle log_9(x)=\frac{3}{2} \iff 9^{\frac{3}{2}}=x \iff 27=x$

4. Sorry about that, thanks for the help.