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Popular >

simplify 72ln(4)-72ln(6)

Solution

simplify

72 ln (4) - 72 ln (6)

Solution

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

+1

Decimal Notation

- 29.19348 \dots

Solution steps

72 ln (4) - 72 ln (6)

Apply log rule:

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

72 ln (4) = ln (4^{72})

= ln (4^{72}) - 72 ln (6)

Apply log rule:

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

72 ln (6) = ln (6^{72})

= ln (4^{72}) - ln (6^{72})

Apply log rule:

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

ln (4^{72}) - ln (6^{72}) = ln (\frac{4 ^{72}}{6 ^{72}})

= ln (\frac{4 ^{72}}{6 ^{72}})

\frac{4 ^{72}}{6 ^{72}} = \frac{2 ^{72}}{3 ^{72}}

= ln (\frac{2 ^{72}}{3 ^{72}})

Combine same powers :

\frac{x ^{n}}{y ^{n}} = (\frac{x}{y})^{n}

= ln ((\frac{2}{3})^{72})

Apply log rule

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

assuming

x \geq 0

= 72 ln (\frac{2}{3})

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Frequently Asked Questions (FAQ)

What is 72ln(4)-72ln(6) ?
The solution to 72ln(4)-72ln(6) is 72ln(2/3)