What is ln((5*8^5)/(2.9)) ?

The solution to ln((5*8^5)/(2.9)) is ln(5)+15ln(2)-ln(2.9)

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simplify ln((5*8^5)/(2.9))

simplify

ln (\frac{5 \cdot 8 ^{5}}{2.9})

ln (5) + 15 ln (2) - ln (2.9)

Decimal Notation

10.94193 \dots

Solution steps

ln (\frac{5 \cdot 8 ^{5}}{2.9})

Apply log rule:

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

ln (\frac{5 \cdot 8 ^{5}}{2.9}) = ln (5 \cdot 8^{5}) - ln (2.9)

= ln (8^{5} \cdot 5) - ln (2.9)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (5 \cdot 8^{5}) = ln (5) + ln (8^{5})

= ln (5) + ln (8^{5}) - ln (2.9)

Apply log rule:

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

ln (8^{5}) = 5 ln (8)

= ln (5) + 5 ln (8) - ln (2.9)

5 ln (8) = 15 ln (2)

= ln (5) + 15 ln (2) - ln (2.9)

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What is ln((5*8^5)/(2.9)) ?
The solution to ln((5*8^5)/(2.9)) is ln(5)+15ln(2)-ln(2.9)