Enter the missing value into the box to complete the ratio comparing 75 centimeters to 3 meters. 1 :__
1 answer:
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Using logarithmic laws: log(a) + log(b) = log(ab)
log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3
Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.
Solving the quadratic we get:
BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.
log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3
Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.
Solving the quadratic we get:
BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.
