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Popular >

simplify ln((10^9)/((1.5)))

Solution

simplify

ln (\frac{1 0 ^{9}}{( 1.5 )})

Solution

9 ln (10) - ln (1.5)

+1

Decimal Notation

20.31780 \dots

Solution steps

ln (\frac{1 0 ^{9}}{( 1.5 )})

Apply log rule:

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

ln (\frac{1 0 ^{9}}{( 1.5 )}) = ln (1 0^{9}) - ln ((1.5))

= ln (1 0^{9}) - ln (1.5)

Apply log rule:

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

ln (1 0^{9}) = 9 ln (10)

= 9 ln (10) - ln (1.5)

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Frequently Asked Questions (FAQ)

What is ln((10^9)/((1.5))) ?
The solution to ln((10^9)/((1.5))) is 9ln(10)-ln(1.5)