What is ln((0.025m^3)/(0.016m^3)) ?

The solution to ln((0.025m^3)/(0.016m^3)) is ln(0.025)-ln(0.016)

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simplify ln((0.025m^3)/(0.016m^3))

simplify

ln (\frac{0.025 m ^{3}}{0.016 m ^{3}})

ln (0.025) - ln (0.016)

Decimal Notation

0.44628 \dots

Solution steps

ln (\frac{0.025 m ^{3}}{0.016 m ^{3}})

Apply log rule:

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

ln (\frac{0.025 m ^{3}}{0.016 m ^{3}}) = ln (0.025 m^{3}) - ln (0.016 m^{3})

= ln (0.025 m^{3}) - ln (0.016 m^{3})

Apply log rule:

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

ln (0.025 m^{3}) = ln (0.025) + ln (m^{3}), ln (0.016 m^{3}) = ln (0.016) + ln (m^{3})

= ln (0.025) + ln (m^{3}) - (ln (m^{3}) + ln (0.016))

Apply log rule:

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

ln (m^{3}) = 3 ln (m)

= ln (0.025) + 3 ln (m) - (ln (0.016) + 3 ln (m))

Apply log rule:

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

ln (m^{3}) = 3 ln (m)

= ln (0.025) + 3 ln (m) - (ln (0.016) + 3 ln (m))

- (ln (0.016) + 3 ln (m)) : - ln (0.016) - 3 ln (m)

= ln (0.025) + 3 ln (m) - ln (0.016) - 3 ln (m)

Simplify

ln (0.025) + 3 ln (m) - ln (0.016) - 3 ln (m) : ln (0.025) - ln (0.016)

= ln (0.025) - ln (0.016)

ln (\frac{15}{12})

- ln (\frac{5.5}{15})

7 lo g_{10} (a) + lo g_{10} (d)

lo g_{2} (3 y) + 4 lo g_{2} (x)

What is ln((0.025m^3)/(0.016m^3)) ?
The solution to ln((0.025m^3)/(0.016m^3)) is ln(0.025)-ln(0.016)