Question

Solve each equation. Show your work please. Part 1​

Answer 1

Answer:

1. x = -10 1/6
2. x = 24 3/5
3. 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