What is 36*ln(9)-36*ln(4) ?

The solution to 36*ln(9)-36*ln(4) is 36ln(9/4)

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simplify 36ln(9)-36ln(4)

simplify

36 \cdot ln (9) - 36 \cdot ln (4)

36 ln (\frac{9}{4})

Decimal Notation

29.19348 \dots

Solution steps

36 ln (9) - 36 ln (4)

Apply log rule:

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

36 ln (9) = ln (9^{36})

= ln (9^{36}) - 36 ln (4)

Apply log rule:

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

36 ln (4) = ln (4^{36})

= ln (9^{36}) - ln (4^{36})

Apply log rule:

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

ln (9^{36}) - ln (4^{36}) = ln (\frac{9 ^{36}}{4 ^{36}})

= ln (\frac{9 ^{36}}{4 ^{36}})

Combine same powers :

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

= ln ((\frac{9}{4})^{36})

Apply log rule

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

assuming

x \geq 0

= 36 ln (\frac{9}{4})

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