What is simplify-10ln(16)+10ln(9) ?

The solution to simplify-10ln(16)+10ln(9) is 10ln(9/16)

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simplify-10ln(16)+10ln(9)

simplify

- 10 ln (16) + 10 ln (9)

10 ln (\frac{9}{16})

Decimal Notation

- 5.75364 \dots

Solution steps

- 10 ln (16) + 10 ln (9)

Apply log rule:

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

10 ln (16) = ln (1 6^{10})

= - ln (1 6^{10}) + 10 ln (9)

Apply log rule:

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

10 ln (9) = ln (9^{10})

= - ln (1 6^{10}) + ln (9^{10})

Apply log rule:

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

ln (9^{10}) - ln (1 6^{10}) = ln (\frac{9 ^{10}}{1 6 ^{10}})

= ln (\frac{9 ^{10}}{1 6 ^{10}})

Combine same powers :

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

= ln ((\frac{9}{16})^{10})

Apply log rule

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

assuming

x \geq 0

= 10 ln (\frac{9}{16})

lo g_{3} (2 z) - lo g_{3} (x)

\frac{8}{12} lo g_{2} (\frac{8}{12}) + \frac{4}{12} lo g_{2} (\frac{4}{12})

lo g_{10} ((19 y)^{6})

lo g_{3} (27 (x^{2} - 49))

lo g_{2} (9) - lo g_{2} (y) + \frac{1}{2} lo g_{2} (x)

What is simplify-10ln(16)+10ln(9) ?
The solution to simplify-10ln(16)+10ln(9) is 10ln(9/16)