What is (7ln(2)-ln(12.8))/(ln(36.1)-ln(22)) ?

The solution to (7ln(2)-ln(12.8))/(ln(36.1)-ln(22)) is (ln(10))/(ln(1.64090…))

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simplify (7ln(2)-ln(12.8))/(ln(36.1)-ln(22))

simplify

\frac{7 ln ( 2 ) - ln ( 12.8 )}{ln ( 36.1 ) - ln ( 22 )}

\frac{ln ( 10 )}{ln ( 1.64090 \dots )}

Decimal Notation

4.64933 \dots

Solution steps

\frac{7 ln ( 2 ) - ln ( 12.8 )}{ln ( 36.1 ) - ln ( 22 )}

Apply log rule:

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

7 ln (2) = ln (2^{7})

= \frac{ln ( 2 ^{7} ) - ln ( 12.8 )}{ln ( 36.1 ) - ln ( 22 )}

Apply log rule:

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

ln (2^{7}) - ln (12.8) = ln (\frac{2 ^{7}}{12.8})

= \frac{ln ( \frac{2 ^{7}}{12.8} )}{ln ( 36.1 ) - ln ( 22 )}

\frac{2 ^{7}}{12.8} = 10

= \frac{ln ( 10 )}{ln ( 36.1 ) - ln ( 22 )}

Apply log rule:

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

ln (36.1) - ln (22) = ln (\frac{36.1}{22})

= \frac{ln ( 10 )}{ln ( \frac{36.1}{22} )}

Divide the numbers:

\frac{36.1}{22} = 1.64090 \dots

= \frac{ln ( 10 )}{ln ( 1.64090 \dots )}

ln (9 e^{2}) + ln (3 e^{- 2})

3 x + 3 ln (x - 1) - 3 ln (2) - 3 ln (x)

- lo g_{10} (5.8 \cdot 1 0^{- 7})

ln (\frac{10}{15})

ln (\frac{x}{2})

What is (7ln(2)-ln(12.8))/(ln(36.1)-ln(22)) ?
The solution to (7ln(2)-ln(12.8))/(ln(36.1)-ln(22)) is (ln(10))/(ln(1.64090…))