What is (25ln(3)-9ln(5))/8+1 ?

The solution to (25ln(3)-9ln(5))/8+1 is (ln((3^{25})/(1953125)))/8+1

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simplify (25ln(3)-9ln(5))/8+1

simplify

\frac{25 ln ( 3 ) - 9 ln ( 5 )}{8} + 1

\frac{ln ( \frac{3 ^{25}}{1953125} )}{8} + 1

Decimal Notation

2.62254 \dots

Solution steps

\frac{25 ln ( 3 ) - 9 ln ( 5 )}{8} + 1

Apply log rule:

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

25 ln (3) = ln (3^{25})

= \frac{ln ( 3 ^{25} ) - 9 ln ( 5 )}{8} + 1

Apply log rule:

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

9 ln (5) = ln (5^{9})

= \frac{ln ( 3 ^{25} ) - ln ( 5 ^{9} )}{8} + 1

Apply log rule:

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

ln (3^{25}) - ln (5^{9}) = ln (\frac{3 ^{25}}{5 ^{9}})

= \frac{ln ( \frac{3 ^{25}}{5 ^{9}} )}{8} + 1

5^{9} = 1953125

= \frac{ln ( \frac{3 ^{25}}{1953125} )}{8} + 1

\frac{1}{144} ln (2)

ln (x^{8} 7 - x)

ln (x + 1) + ln (y)

- 4 ln (u) + 2 ln (y)

- lo g_{10} (3.4 \cdot 1 0^{- 6})

What is (25ln(3)-9ln(5))/8+1 ?
The solution to (25ln(3)-9ln(5))/8+1 is (ln((3^{25})/(1953125)))/8+1