What is (ln(10000)-ln(150))/(ln(70000)-ln(150)) ?

The solution to (ln(10000)-ln(150))/(ln(70000)-ln(150)) is (ln(200/3))/(ln(1400/3))

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simplify (ln(10000)-ln(150))/(ln(70000)-ln(150))

simplify

\frac{ln ( 10000 ) - ln ( 150 )}{ln ( 70000 ) - ln ( 150 )}

\frac{ln ( \frac{200}{3} )}{ln ( \frac{1400}{3} )}

Decimal Notation

0.68336 \dots

Solution steps

\frac{ln ( 10000 ) - ln ( 150 )}{ln ( 70000 ) - ln ( 150 )}

Apply log rule:

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

ln (10000) - ln (150) = ln (\frac{10000}{150})

= \frac{ln ( \frac{10000}{150} )}{ln ( 70000 ) - ln ( 150 )}

Cancel the common factor:

50

= \frac{ln ( \frac{200}{3} )}{ln ( 70000 ) - ln ( 150 )}

Apply log rule:

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

ln (70000) - ln (150) = ln (\frac{70000}{150})

= \frac{ln ( \frac{200}{3} )}{ln ( \frac{70000}{150} )}

Cancel the common factor:

50

= \frac{ln ( \frac{200}{3} )}{ln ( \frac{1400}{3} )}

3 lo g_{7} (u) + 9 lo g_{7} (v)

ln (\frac{2 a ^{3}}{b ^{4}})

lo g_{5} (4 x^{2})

ln ((x + h)^{2} + (x + h) + 1) - ln (x^{2} + x + 1)

ln (\frac{2 \cdot 22.91}{0.01173})

What is (ln(10000)-ln(150))/(ln(70000)-ln(150)) ?
The solution to (ln(10000)-ln(150))/(ln(70000)-ln(150)) is (ln(200/3))/(ln(1400/3))