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Popular >

simplify ln(9/(sqrt(9-8)))

Solution

simplify

ln (\frac{9}{9 - 8})

Solution

2 ln (3)

+1

Decimal Notation

2.19722 \dots

Solution steps

ln (\frac{9}{9 - 8})

Apply log rule:

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

ln (\frac{9}{9 - 8}) = ln (9) - ln (9 - 8)

= ln (9) - ln (9 - 8)

ln (9 - 8) = 0

= ln (9) - 0

ln (9) - 0 = ln (9)

= ln (9)

Rewrite

9

in power-base form:

9 = 3^{2}

= ln (3^{2})

Apply log rule:

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

ln (3^{2}) = 2 ln (3)

= 2 ln (3)

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Frequently Asked Questions (FAQ)

What is ln(9/(sqrt(9-8))) ?
The solution to ln(9/(sqrt(9-8))) is 2ln(3)