What is (ln(60000)-ln(100))/(ln(75000)-ln(100)) ?

The solution to (ln(60000)-ln(100))/(ln(75000)-ln(100)) is (ln(600))/(ln(750))

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simplify (ln(60000)-ln(100))/(ln(75000)-ln(100))

simplify

\frac{ln ( 60000 ) - ln ( 100 )}{ln ( 75000 ) - ln ( 100 )}

\frac{ln ( 600 )}{ln ( 750 )}

Decimal Notation

0.96629 \dots

Solution steps

\frac{ln ( 60000 ) - ln ( 100 )}{ln ( 75000 ) - ln ( 100 )}

Apply log rule:

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

ln (60000) - ln (100) = ln (\frac{60000}{100})

= \frac{ln ( \frac{60000}{100} )}{ln ( 75000 ) - ln ( 100 )}

Divide the numbers:

\frac{60000}{100} = 600

= \frac{ln ( 600 )}{ln ( 75000 ) - ln ( 100 )}

Apply log rule:

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

ln (75000) - ln (100) = ln (\frac{75000}{100})

= \frac{ln ( 600 )}{ln ( \frac{75000}{100} )}

Divide the numbers:

\frac{75000}{100} = 750

= \frac{ln ( 600 )}{ln ( 750 )}

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

What is (ln(60000)-ln(100))/(ln(75000)-ln(100)) ?
The solution to (ln(60000)-ln(100))/(ln(75000)-ln(100)) is (ln(600))/(ln(750))