SOLUTION: 1. There is one x satisfying 5^(−3x−2)=1/78125. Use the rules of exponentiation and logarithms to find this number. The value of x is... 2. There is one x satisf

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1. There is one x satisfying 5^(−3x−2)=1/78125. Use the rules of exponentiation and logarithms to find this number. The value of x is... 2. There is one x satisf      Log On


   

Question 501109: 1. There is one x satisfying 5^(−3x−2)=1/78125. Use the rules of exponentiation and logarithms to find this number.
The value of x is...
2. There is one x satisfying log3(4x−8)=1. Use the rules of exponentiation and logarithms to find this number.
The value of x is...
Answer by lwsshak3(11628) About Me  (Show Source):
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1. There is one x satisfying 5^(−3x−2)=1/78125. Use the rules of exponentiation and logarithms to find this number.
The value of x is...
2. There is one x satisfying log3(4x−8)=1. Use the rules of exponentiation and logarithms to find this number.
The value of x is..
**
1. 5^(−3x−2)=1/78125=78125^-1
Take log of both sides
(-3x-2)log 5=(-1) log 78125
(-3x-2)/(-1)=- log 78125/log 5
3x+2=-7
3x=-9
x=-3
Check:
5^(−3x−2)=5^-7=12.8*10^-6
1/78125=78125^-1=12.8*10^-6
..
2. log3(4x−8)=1
convert to exponential form: base(3) raised to log of number(1)=number(4x-8)
3^1=4x-8
3=4x-8
4x=11
x=11/4
Check:
log3(4x-8)=log(11-8)=log3(3)=1 (log of any base to its base=1)