What is ln(1/(f(a)x^a)) ?

The solution to ln(1/(f(a)x^a)) is -aln(x)-ln(a)-ln(f)

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simplify ln(1/(f(a)x^a))

simplify

ln (\frac{1}{f ( a ) x ^{a}})

- a ln (x) - ln (a) - ln (f)

Solution steps

ln (\frac{1}{f ( a ) x ^{a}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{f ( a ) x ^{a}}) = ln (1) - ln (f (a) x^{a})

= ln (1) - ln (a f x^{a})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (f a x^{a}) = ln (f) + ln (a) + ln (x^{a})

= ln (1) - (ln (a) + ln (x^{a}) + ln (f))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{a}) = a ln (x)

= ln (1) - (ln (f) + ln (a) + a ln (x))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (a ln (x) + ln (a) + ln (f))

0 - (ln (f) + ln (a) + a ln (x)) = - (ln (f) + ln (a) + a ln (x))

= - (a ln (x) + ln (a) + ln (f))

Distribute parentheses

= - (a ln (x)) - (ln (a)) - (ln (f))

Apply minus-plus rules

+ (- a) = - a

= - a ln (x) - ln (a) - ln (f)

ln (2 + x) + ln (2 - x)

ln (\frac{10}{0.02375})

- lo g_{10} (5.2 \cdot 1 0^{- 6})

ln (29) - ln (2)

ln (12) + ln (27)

What is ln(1/(f(a)x^a)) ?
The solution to ln(1/(f(a)x^a)) is -aln(x)-ln(a)-ln(f)