SOLUTION: 2. Solve the following equations, giving exact values if possible. a. 9^x-1 = (1/3)^2x b. ln(x+2)=3 c. log27(x)=1-log27(x-0.4) d. logb6=1/2

Algebra ->  Functions -> SOLUTION: 2. Solve the following equations, giving exact values if possible. a. 9^x-1 = (1/3)^2x b. ln(x+2)=3 c. log27(x)=1-log27(x-0.4) d. logb6=1/2      Log On


   

Question 1102750: 2. Solve the following equations, giving exact values if possible.
a. 9^x-1 = (1/3)^2x
b. ln(x+2)=3
c. log27(x)=1-log27(x-0.4)
d. logb6=1/2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
9%5E%28x-1%29+=+%281%2F3%29%5E%282x%29
%283%5E2%29%5E%28x-1%29=%283%5E%28-1%29%29%5E%282x%29
3%5E%282%28x-1%29%29=3%5E%28-2x%29
2x-2=-2x
4x=2
x=1%2F2
.
.
.
ln%28x%2B2%29=3
x%2B2=e%5E3
x=e%5E3-2
.
.
.
log%2827%2C%28x%29%29=1-log%2827%2C%28x-0.4%29%29
log%2827%2C%28x%29%29%2Blog%2827%2C%28x-0.4%29%29=1
log%2827%2C%28x%28x-0.4%29%29%29=1
x%28x-0.4%29=27
x%5E2-0.4x=27
x%5E2-0.4x%2B0.04=27.04
%28x-0.2%29%5E2=0+%2B-+5.2
x=0.2+%2B-+5.2
x must be positive so,
x=5.4
.
.
.
log%28b%2C%286%29%29=1%2F2
log%28%286%29%29%2Flog%28%28b%29%29=1%2F2
log%28%28b%29%29=log%28%286%29%29%2F%281%2F2%29
log%28%28b%29%29=2%2Alog%28%286%29%29
log%28%28b%29%29=log%28%2836%29%29
b=36