Answer:
- x = -10 1/6
- x = 24 3/5
- x = -7 1/4
Step-by-step explanation:
The relevant rules of logarithms are ...
log(a)+log(b) = log(ab)
log(a)-log(b) = log(a/b)
The base of the logarithm doesn't matter, as long as all bases are the same.
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In each case, we can simplify the left side to a single log, then take the antilog and finish solving the linear equation.
1. log(3-x) +log(6) = log(79)
log(6(3-x)) = log(79)
6(3 -x) = 79
3 -x = 79/6
x = 3 -79/6
x = -10 1/6
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2. log(5x +3) -log(2) = log(63)
log((5x+3)/2) = log(63)
(5x +3)/2 = 63
5x +3 = 126
5x = 123
x = 24.6
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3. log(-4x -7) +log(2) = log(44)
log(2(-4x-7)) = log(44)
2(-4x -7) = 44
4x +7 = -22
4x = -29
x = -7 1/4
