What is (ln(1.4)-5ln(1.05))/(2ln(1.05)) ?

The solution to (ln(1.4)-5ln(1.05))/(2ln(1.05)) is (ln(1.09693…))/(2ln(1.05))

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simplify (ln(1.4)-5ln(1.05))/(2ln(1.05))

simplify

\frac{ln ( 1.4 ) - 5 ln ( 1.05 )}{2 ln ( 1.05 )}

\frac{ln ( 1.09693 \dots )}{2 ln ( 1.05 )}

Decimal Notation

0.94815 \dots

Solution steps

\frac{ln ( 1.4 ) - 5 ln ( 1.05 )}{2 ln ( 1.05 )}

Apply log rule:

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

5 ln (1.05) = ln (1.0 5^{5})

= \frac{ln ( 1.4 ) - ln ( 1.0 5 ^{5} )}{2 ln ( 1.05 )}

Apply log rule:

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

ln (1.4) - ln (1.0 5^{5}) = ln (\frac{1.4}{1.0 5 ^{5}})

= \frac{ln ( \frac{1.4}{1.0 5 ^{5}} )}{2 ln ( 1.05 )}

\frac{1.4}{1.0 5 ^{5}} = 1.09693 \dots

= \frac{ln ( 1.09693 \dots )}{2 ln ( 1.05 )}

lo g_{\frac{1}{2}} (\frac{1}{2} x)

ln (x^{3}) + ln (y^{3})

lo g_{10} (2 x^{5} (1 - x)^{4} (1 - 2 x)^{5})

ln (e^{36} - 1) - ln (36 e^{36})

What is (ln(1.4)-5ln(1.05))/(2ln(1.05)) ?
The solution to (ln(1.4)-5ln(1.05))/(2ln(1.05)) is (ln(1.09693…))/(2ln(1.05))