Angie was working on solving the exponential equation 23^x = 6; however she isn't sure where to start. Describe to Angie how to solve this equation and how solving it would be different if the bases were equal.

The only thing I need help with is how solving it would be different if the bases were equal

Question

Angie was working on solving the exponential equation 23^x = 6; however she isn't sure where to start. Describe to Angie how to solve this equation and how solving it would be different if the bases were equal.

The only thing I need help with is how solving it would be different if the bases were equal

unanimoose · Answer

If the bases were equal you would just need to compare the exponent.

anonymous · Answer

Okay. How would that look?

unanimoose · Answer

Okay say you had: $$9^x = 16$$

unanimoose · Answer

Sorry the site lagged out for a sec.

unanimoose · Answer

Ok so we can rewrite this as:

$$3^3x = 4^2$$

unanimoose · Answer

Woops, hold on.

unanimoose · Answer

Let me use a different example.

unanimoose · Answer

$$64^x = 16$$

unanimoose · Answer

Ok, we can rewrite this as:

$$4^3x = 4^2$$

unanimoose · Answer

That x is meant to be part of the exponent but Latex didn't let me do that.

unanimoose · Answer

So since the bases are the same we can just compare the exponent and just solve for: 3x = 2

Since the bases are equivalent and nothing needs to be done with them. @Tarynrachelle

unanimoose · Answer

Hope this helps.

anonymous · Answer

Okay.. Let me see if I get it haha. Thank you :)

unanimoose · Answer

Np. :)