What is ln(4^3+4)-ln(8*(4)^3+15(4)) ?

The solution to ln(4^3+4)-ln(8*(4)^3+15(4)) is ln(17/143)

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simplify ln(4^3+4)-ln(8*(4)^3+15(4))

simplify

ln (4^{3} + 4) - ln (8 \cdot (4)^{3} + 15 (4))

ln (\frac{17}{143})

Decimal Notation

- 2.12963 \dots

Solution steps

ln (4^{3} + 4) - ln (8 (4)^{3} + 15 (4))

Apply log rule:

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

ln (4^{3} + 4) - ln (4^{3} \cdot 8 + 15 (4)) = ln (\frac{4 ^{3} + 4}{4 ^{3} \cdot 8 + 15 \cdot 4})

= ln (\frac{4 ^{3} + 4}{8 \cdot 4 ^{3} + 15 \cdot 4})

\frac{4 ^{3} + 4}{8 \cdot 4 ^{3} + 15 ( 4 )} = \frac{17}{143}

= ln (\frac{17}{143})

ln (\frac{327.15}{243.15})

lo g_{3} (\frac{x y}{3})

ln (- a \cdot e^{- t})

ln (e n)

10 lo g_{10} (\frac{5 \cdot 1 0 ^{- 6}}{1 0 ^{- 12}})

What is ln(4^3+4)-ln(8*(4)^3+15(4)) ?
The solution to ln(4^3+4)-ln(8*(4)^3+15(4)) is ln(17/143)