Question

How do you solve `3(5)^(2x−3) = 6`?

Answer 1

`x=ln(250)/ln(25)`

Explanation:

Isolate the exponential `5^(2x-3)` by dividing both sides by `3,` yielding

`5^(2x-3)=2`

Furthermore, recall that `x^(a-b)=x^a/x^b,` so `5^(2x-3)=5^(2x)/5^3=5^(2x)/125`

`5^(2x)/125=2`

`5^(2x)=250`

Now, apply the natural logarithm to both sides.

`ln(5^(2x))=ln(250)`

Recall that `ln(a^b)=blna,` so `ln(5^(2x))=2xln(5)`

`2xln(5)=ln(250)`

Now, solve for `x.` This will be much simpler now as it is not in an exponent or logarithm.

`2x=ln(250)/ln(5)`

`x=ln(250)/(2ln5)`

`x=ln(250)/ln(25)` as `2ln5=ln(5^2)=ln(25)`