Solving Exponential Equations

Hey everyone it's Chris and i will be blogging about our class today, on how to solve exponential equations.

Exponent Rules: *Remember*

• a^m aⁿ = a^m+n

• a^m/aⁿ = a^m-n

• (a^m)ⁿ = a^mn

• (ⁿ√a)^m = a^m/n

• 1/a^m = a^-m

• a^-m = 1/a^m

• a⁰ = 1

Steps to solving Exponential Equations:

1) Make the bases on each side equal to one and other.

2) Cancel the same bases.

3) Solve the remaining exponent equation.

Examples:

• Solve 3^2x–1 = 27.

In this case, I have an exponential on one side of the "equals" and a number on the other. I can solve the equation if I can express the "27" as a power of 3. Since 27 = 3³, then I can convert and proceed with the solution:

3^2x–1 = 27
3^2x–1 = 3³ <-- First step i made the bases on each side equal.
2x – 1 = 3 <-- Second step i canceled the bases that were the same.
2x = 4 <-- And last step i solved for x.

x = 2

Example 2:

• Solve 3^{x^2–3x} = 81.

3^{x^2–3x} = 81
3^{x^2–3x} = 3^{4 <-- I first got the bases the same.}
x² – 3x = 4 <-- I next canceled the same bases.
x² – 3x – 4 = 0 <-- Next i moved the 4 over to the other side in order to factor the equation.
(x – 4)(x + 1) = 0 <-- I then factored the equation out.

x = –1, 4 <-- I then equated each side to 0 from the factored equation and solved for x.


Hopefully this helped break it down even more for you guys, if you are still struggling this this i recommend you look up some videos on youtube as they are very helpful! Goodluck!