What is 29ln(8)-13ln(4) ?

The solution to 29ln(8)-13ln(4) is 61ln(2)

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simplify 29ln(8)-13ln(4)

simplify

29 ln (8) - 13 ln (4)

61 ln (2)

Decimal Notation

42.28197 \dots

Solution steps

29 ln (8) - 13 ln (4)

Apply log rule:

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

29 ln (8) = ln (8^{29})

= ln (8^{29}) - 13 ln (4)

Apply log rule:

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

13 ln (4) = ln (4^{13})

= ln (8^{29}) - ln (4^{13})

Apply log rule:

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

ln (8^{29}) - ln (4^{13}) = ln (\frac{8 ^{29}}{4 ^{13}})

= ln (\frac{8 ^{29}}{4 ^{13}})

\frac{8 ^{29}}{4 ^{13}} = 2^{61}

= ln (2^{61})

Apply log rule

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

assuming

x \geq 0

= 61 ln (2)

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