# Exponents with Variables

#### Rae Kirk

##### New member
Can’t find info on how to solve exponents with variables when bases are different.

(5^x)(3^(1-x))=12

#### MarkFL

##### Super Moderator
Staff member
Hello, and welcome to FMH!

I'd write the equation as:

$$\displaystyle \left(\frac{5}{3}\right)^x=4$$

Now, convert from exponential to logarithmic form...what do you get?

#### Rae Kirk

##### New member
That’s it!! I was making it too complicated. Thank you so much. What a great support group.

#### JeffM

##### Elite Member
Mark's approach is elegant, but you can just start by immediately going to logs.

$$\displaystyle (5^x)(3^{(1-x)}) = 12 \implies log\{(5^x)(3^{(1-x)})\} = log(12).$$

It is a bit longer, but it is totally mechanical.

#### Jomo

##### Elite Member
Hello, and welcome to FMH!

I'd write the equation as:

$$\displaystyle \left(\frac{5}{3}\right)^x=4$$

Now, convert from exponential to logarithmic form...what do you get?
Even low level math can look beautiful. Nicely done!