Lesson 6.7 Solving Exponential Equations

Lesson 6.7 Solving Exponential Equations

Type 1: Same base on both sides

• Ignore the base

• Set the exponents equal to each other

• Solve

Multiple Choice

 $2^x=2^{\left(5x-80\right)}$  

•  $x=-11$  

•  $x=20$  

•  $x=4$  

•  $x=-16$  

What if they don't have the same base?

• Can you change one of them to have the same base as the other?

Multiple Choice

 $7^3=49^{\left(x+5\right)}$  

•  $x=5$  

•  $x=-2$  

•  $x=-\frac{7}{2}$  

Type 2: Exponent only on 1 side

• Change to logarithmic form

• Use change of base formula to solve

Multiple Choice

 $10^x=1500$  

•  $x=150$  

•  $x=10$  

•  $x=3.18$  

Multiple Choice

 $5^{4x}=2115$  

•  $x=19.03$  

•  $x=1.19$  

•  $x=4.78$  

•  $x=12.98$  

Multiple Choice

 $10^x+8=1008$  

•  $x=10$  

•  $x=3$  

•  $x=8$  

•  $x=100$  

Multiple Choice

 $7^{\left(x+10\right)}-8=6$  

•  $x=-7.374$  

•  $x=-8.643$  

•  $x=-7.360$  

•  $x=-8.853$