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Step-by-step explanation:

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  x ≈ -1.159

Step-by-step explanation:

We assume you want to solve ...

  5^(2x+4) = 15

Take the base-5 log of both sides, then solve the resulting linear equation. If you need, you can use the change of base formula to find the needed log.

  2x +4 = log₅(15)

  2x = log₅(15) -4 . . . . . . subtract 4

  x = (log₅(15) -4)/2

Using the change of base formula:

  log₅(15) = log(15)/log(5)

  x = (log(15)/log(5) -4)/2

  x = log(15)/(2log(5)) -2 . . . . use the distributive property

  x = log(15)/log(25) -2 ≈ -1.1586969 . . . . simplify the denominator a bit*

  x ≈ -1.159

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* We suppose that "simplest form" might have this as a single term with logarithms having all powers taken out. That is, it might be ...

  x = (log(15) -4log(5))/(2log(5))

In addition to the two logarithms, evaluating this requires 2 multiplications, a sum, and a division. Compare to the expression we used, which requires a division and a sum in addition to two logarithms. We prefer the expression that is simpler to evaluate.