What is ln(64)+ln(7)-5ln(2) ?

The solution to ln(64)+ln(7)-5ln(2) is ln(14)

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simplify ln(64)+ln(7)-5ln(2)

simplify

ln (64) + ln (7) - 5 ln (2)

ln (14)

Decimal Notation

2.63905 \dots

Solution steps

ln (64) + ln (7) - 5 ln (2)

Apply log rule:

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

ln (64) + ln (7) = ln (64 \cdot 7)

= ln (64 \cdot 7) - 5 ln (2)

Multiply the numbers:

64 \cdot 7 = 448

= ln (448) - 5 ln (2)

Apply log rule:

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

5 ln (2) = ln (2^{5})

= ln (448) - ln (2^{5})

Apply log rule:

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

ln (448) - ln (2^{5}) = ln (\frac{448}{2 ^{5}})

= ln (\frac{448}{2 ^{5}})

\frac{448}{2 ^{5}} = 14

= ln (14)

- ln (75) - 3 ln (\frac{15}{22})

ln (0.3 e^{4})

2 ln (5 x^{3}) + ln (2 x^{2})

ln (\frac{\frac{1}{2}}{0.144})

\frac{25 ln ( 3 ) - 9 ln ( 5 )}{8} + 1