Pre Calculus

Question

Given the exponential equation:(5/3)^6x+2=(9/25)^-x+2, find a common base and solve for x.
a) -2/3

b) -3/2

c) 3/2

d) 2/3

Answer 1

The end value here should be x = -3/2

To find that you want to get a common base for each side so that you can compare the exponents. The key trick to keep in mind when doing so is that

(9/25) = (3/5)^2

and then

(3/5)^2 = (5/3)^(-2)

i hope that helps you get moving in a good direction on this one! feel free to reach out if you have any additional questions beyond that! :)

Answer 2

Here's a hint to get you started.  The left side can be written as

 ...

(3/5)^[-2(3x+1)] and this can, in turn, be expressed as (9/25)^[-(3x+1)].    ⇐ error corrected...thanks, Norbert

 

Now we'll have the bases the same on each side of the original exponential equation (having reformatted the lefthand side).

 

Therefore we can set the exponents equal!