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scoray [572]
3 years ago
10

Log x - log 6 = 2 log 4

Mathematics
1 answer:
mylen [45]3 years ago
7 0

log(<em>x</em>) - log(6) = 2 log(4)

Condense the left side, using the property log(<em>a</em>) - log(<em>b</em>) = log(<em>a</em>/<em>b</em>) (if <em>b</em> ≠ 0):

log(<em>x</em> / 6) = 2 log(4)

Rewrite the right side, using the property <em>n</em> log(<em>a</em>) = log(<em>aⁿ </em>):

log(<em>x</em> / 6) = log(4²)

log(<em>x</em> / 6) = log(16)

Cancel the logarithms (i.e. take the exponential of both sides):

exp(log(<em>x </em>/ 6)) = exp(log(16))

<em>x</em> / 6 = 16

Solve for <em>x</em> :

<em>x</em> = 6 × 16

<em>x</em> = 96

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