Question

Find the numerical value of the log expression.

log a = -10
log b = -10
log
a467
log c = 15

Answer 1

150

Explanation:

You want the numerical value for log(a, b, c) = (-10, -10, 15) of ...

`\log\frac{\sqrt[3]{c^8}}{a^4b^7}`

Rules of logarithms

The applicable rule of logarithms are ...

log(ab) = log(a) +log(b)

log(a^b) = b·log(a)

log(a/b) = log(a) -log(b)

Radicals

The applicable rule for radicals is ...

`\sqrt[n]{a^m}=a^{(m)/(n)}`

Expanded

Using the above rules, we can rewrite the logarithm as ...

`\log\frac{\sqrt[3]{c^8}}{a^4b^7}=(8)/(3)\log(c)-(4\log(a)+7\log(b))\\\\=(8)/(3)(15)-(4(-10)+7(-10))=40+(4+7)(10)=\boxed{150}`

The numerical value of the log expression is 150.

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