What is (ln(7)-ln(1.02))/(3ln(1.02)) ?

The solution to (ln(7)-ln(1.02))/(3ln(1.02)) is (ln(6.86274…))/(3ln(1.02))

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simplify (ln(7)-ln(1.02))/(3ln(1.02))

simplify

\frac{ln ( 7 ) - ln ( 1.02 )}{3 ln ( 1.02 )}

\frac{ln ( 6.86274 \dots )}{3 ln ( 1.02 )}

Decimal Notation

32.42175 \dots

Solution steps

\frac{ln ( 7 ) - ln ( 1.02 )}{3 ln ( 1.02 )}

Apply log rule:

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

ln (7) - ln (1.02) = ln (\frac{7}{1.02})

= \frac{ln ( \frac{7}{1.02} )}{3 ln ( 1.02 )}

Divide the numbers:

\frac{7}{1.02} = 6.86274 \dots

= \frac{ln ( 6.86274 \dots )}{3 ln ( 1.02 )}

6 ln (3) - 6 ln (2)

lo g_{e} (8) + 9 lo g_{e} (π) - lo g_{e} (5)

- ln (\frac{25}{16})

lo g_{9} (u \cdot v \cdot w)

ln (3) \frac{1}{2}

What is (ln(7)-ln(1.02))/(3ln(1.02)) ?
The solution to (ln(7)-ln(1.02))/(3ln(1.02)) is (ln(6.86274…))/(3ln(1.02))