Exponential Equations Review

Same Base

100

2^(x+1)=2^9

x=8

200

5^(4n+5)=5^(n-7)

n=-4

300

9^(3x-7)=9^(5-x)

x=3

400

6^(5n-6)=6^(6n+3)

n=-9

500

4^(6y-2)=4^(2y-22)

y=-5

Same Base w/ Multiplying

100

3^k*3^(k+2)=3^(5k-1)

k=1

200

5^x*5^(2x+3)=5^(-x-9)

x=-3

300

2^(w+4)*2^(4w+6)=2^(2w+1)

w=-3

400

6^(3x)*6^3=6^2*6^(-3x)

x=-1/6 or -0.166667

500

10^(-4)*10^9=10^(v+4)*10^(2v-11)

v=4

Change One Base

100

2^(p-7)=8

p=10

200

6^(2x-10)=36

x=6

300

7^(4x+11)=1/7

x=-3

400

27^(2x+6)=3^(2x)

x=-9/2 or -4.5

500

4^(y+2)=16^(y-3)

y=8

Change Multiple Bases

100

4^(3x)=8^(x-1)

x=-1

200

81^(2x+5)=(1/3)^(2x)

x=-2

300

27^(2x)=243^(x-2)

x=-10

400

8^(2a-1)=32^(2a+1)

a=-2

500

49^(p+1)=343^(2p)

p=1/2 or 0.5

Change Bases w/ Multiplying

100

16*2^(6m)=2^(3m-8)

m=-4

200

256^y*16^(y-1)=4^(2y-22)

y=-5

300

(1/9)^a*(1/3)^a=3^(16-a)

a=-8

400

36^(n-3)*216^n=216^(2n+1)

n=-9

500

(1/4)^(2x+3)*32^(2x-1)=8^(4x)*(1/128)^(2-3x)

x=1/9 or 0.1111