What is ln(13)+7ln(a)-11ln(b)+ln(c) ?

The solution to ln(13)+7ln(a)-11ln(b)+ln(c) is ln((13a^7c)/(b^{11)})

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simplify ln(13)+7ln(a)-11ln(b)+ln(c)

simplify

ln (13) + 7 ln (a) - 11 ln (b) + ln (c)

ln (\frac{13 a ^{7} c}{b ^{11}})

Solution steps

ln (13) + 7 ln (a) - 11 ln (b) + ln (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

7 ln (a) = ln (a^{7})

= ln (13) + ln (a^{7}) - 11 ln (b) + ln (c)

Apply log rule:

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

ln (13) + ln (a^{7}) = ln (13 a^{7})

= ln (13 a^{7}) - 11 ln (b) + ln (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

11 ln (b) = ln (b^{11})

= ln (13 a^{7}) - ln (b^{11}) + ln (c)

Apply log rule:

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

ln (13 a^{7}) - ln (b^{11}) = ln (\frac{13 a ^{7}}{b ^{11}})

= ln (\frac{13 a ^{7}}{b ^{11}}) + ln (c)

Apply log rule:

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

ln (\frac{13 a ^{7}}{b ^{11}}) + ln (c) = ln (c \frac{13 a ^{7}}{b ^{11}})

= ln (c \frac{13 a ^{7}}{b ^{11}})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{13 a ^{7} c}{b ^{11}})

lo g_{10} (0.48 5^{\frac{1}{4}} \cdot 0.3 6^{\frac{1}{3}})

ln (3 x) - 2 ln (x)

ln (a) + ln (\frac{1}{2 b}) - b (\frac{1}{2 b})^{2}

e lo g_{3} (\frac{1}{81}) + lo g_{\frac{1}{3}} (\frac{1}{61})_{e}

ln (\frac{4}{e})

What is ln(13)+7ln(a)-11ln(b)+ln(c) ?
The solution to ln(13)+7ln(a)-11ln(b)+ln(c) is ln((13a^7c)/(b^{11)})