SOLUTION: 1. log(3)x=-2 (answers: -8, -6, 1/9, 9) 2. 7^x=8 (answers:.06, .94, .98, 1.07)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1. log(3)x=-2 (answers: -8, -6, 1/9, 9) 2. 7^x=8 (answers:.06, .94, .98, 1.07)       Log On


   

Question 116158: 1. log(3)x=-2
(answers: -8, -6, 1/9, 9)
2. 7^x=8
(answers:.06, .94, .98, 1.07)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1
log%283%2C%28x%29%29=-2 Start with the given equation.


3%5E%28-2%29=x Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


1%2F3%5E2=x Rewrite 3%5E%28-2%29 as 1%2F3%5E2


1%2F9=x Evaluate 3%5E2 to get 9

So our answer is x=1%2F9



#2

7%5Ex=8 Start with the given equation.


log%2810%2C%287%5Ex%29%29=log%2810%2C%288%29%29 Take the log of both sides.



x%2Alog%2810%2C%287%29%29=log%2810%2C%288%29%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 .



x=log%2810%2C%288%29%29%2Flog%2810%2C%287%29%29 Divide both sides by log%2810%2C%287%29%29 to isolate x


x=1.06862156132407 Now simply use a calculator to evaluate the right side

So our approximate answer is x=1.07