What is ln(c(x^a)/(z^b)) ?

The solution to ln(c(x^a)/(z^b)) is ln(c)++aln(x)-bln(z)

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simplify ln(c(x^a)/(z^b))

simplify

ln (c \frac{x ^{a}}{z ^{b}})

ln (c) + + a ln (x) - b ln (z)

Solution steps

ln (c \frac{x ^{a}}{z ^{b}})

Apply log rule:

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

ln (c \frac{x ^{a}}{z ^{b}}) = ln (c) + ln (\frac{x ^{a}}{z ^{b}})

= ln (c) + ln (\frac{x ^{a}}{z ^{b}})

Apply log rule:

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

ln (\frac{x ^{a}}{z ^{b}}) = ln (x^{a}) - ln (z^{b})

= ln (c) + + ln (x^{a}) - ln (z^{b})

Apply log rule:

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

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

= ln (c) + + a ln (x) - ln (z^{b})

Apply log rule:

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

ln (z^{b}) = b ln (z)

= ln (c) + + a ln (x) - b ln (z)

\frac{1}{2} ln (\frac{120}{500})

ln (5) + \frac{1}{3} ln (8)

5 lo g_{2} (x) + 5 lo g_{2} (y)

9 lo g_{10} (2^{2}) - 9 lo g_{10} (5^{2})

lo g_{3} (7) - lo g_{3} (10)

What is ln(c(x^a)/(z^b)) ?
The solution to ln(c(x^a)/(z^b)) is ln(c)++aln(x)-bln(z)