# How do you solve #5^(x^2+2x)=125#?

##### 2 Answers

Dec 2, 2016

#### Explanation:

*To solve the equation* *for variable* *we must apply the logarithm conversion formula.*

**logarithm to exponential conversion:**

**calculations**

#5^(x^2+2x)=125\rArr\log_5(125)=x^2+2x# - You're going to need a calculator to solve the left side's logarithm, but you should get the following:

#3=x^2+2x# - Now subtract 3 from both sides to form a quadratic equation:

#0=x^2+2x-3# - You should get roots of -3 and 1.
#\rArr(x+3)(x-1)#

*Therefore,*

Dec 4, 2016

#### Explanation:

Another way to approach this is to realize that

#5^(x^2+2x)=5^3#

We now have two equal bases, each to a power. Since these are equal, we can say that their exponents must be equal. (We could write a rule for this and say that if

So we know that

#x^2+2x=3#

Solving like a regular quadratic:

#x^2+2x-3=0#

#(x+3)(x-1)=0#

So