Exponents with Variables

[Rae Kirk]

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

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

 

[MarkFL]

Hello, and welcome to FMH!

I'd write the equation as:

[MATH]\left(\frac{5}{3}\right)^x=4[/MATH]
Now, convert from exponential to logarithmic form...what do you get?

 

[Rae Kirk]

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

 

[JeffM]

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

[MATH](5^x)(3^{(1-x)}) = 12 \implies log\{(5^x)(3^{(1-x)})\} = log(12).[/MATH]
It is a bit longer, but it is totally mechanical.

 

[Steven G]

Hello, and welcome to FMH!

I'd write the equation as:

[MATH]\left(\frac{5}{3}\right)^x=4[/MATH]
Now, convert from exponential to logarithmic form...what do you get?

Even low level math can look beautiful. Nicely done!