What is ln(2^3+4)-ln(8*(2)^3+15(2)) ?

The solution to ln(2^3+4)-ln(8*(2)^3+15(2)) is ln(6/47)

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simplify ln(2^3+4)-ln(8*(2)^3+15(2))

simplify

ln (2^{3} + 4) - ln (8 \cdot (2)^{3} + 15 (2))

ln (\frac{6}{47})

Decimal Notation

- 2.05838 \dots

Solution steps

ln (2^{3} + 4) - ln (8 (2)^{3} + 15 (2))

Apply log rule:

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

ln (2^{3} + 4) - ln (2^{3} \cdot 8 + 15 (2)) = ln (\frac{2 ^{3} + 4}{2 ^{3} \cdot 8 + 15 \cdot 2})

= ln (\frac{2 ^{3} + 4}{8 \cdot 2 ^{3} + 15 \cdot 2})

\frac{2 ^{3} + 4}{8 \cdot 2 ^{3} + 15 ( 2 )} = \frac{6}{47}

= ln (\frac{6}{47})

3 \cdot \frac{- 2 ln ( 11 ) + 4 ln ( 3 )}{20}

14 + lo g_{10} (\frac{0.118}{5})

ln (\frac{2 x}{1 + x ^{2}})

lo g_{4} ((\frac{12}{1 1 ^{3}})^{6})

ln (3) - \frac{2}{3} ln (2)

What is ln(2^3+4)-ln(8*(2)^3+15(2)) ?
The solution to ln(2^3+4)-ln(8*(2)^3+15(2)) is ln(6/47)