What is (5ln(7))/(3ln(10)-ln(7)) ?

The solution to (5ln(7))/(3ln(10)-ln(7)) is (5ln(7))/(ln(1000/7))

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simplify (5ln(7))/(3ln(10)-ln(7))

simplify

\frac{5 ln ( 7 )}{3 ln ( 10 ) - ln ( 7 )}

\frac{5 ln ( 7 )}{ln ( \frac{1000}{7} )}

Decimal Notation

1.96087 \dots

Solution steps

\frac{5 ln ( 7 )}{3 ln ( 10 ) - ln ( 7 )}

Apply log rule:

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

3 ln (10) = ln (1 0^{3})

= \frac{5 ln ( 7 )}{ln ( 1 0 ^{3} ) - ln ( 7 )}

Apply log rule:

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

ln (1 0^{3}) - ln (7) = ln (\frac{1 0 ^{3}}{7})

= \frac{5 ln ( 7 )}{ln ( \frac{1 0 ^{3}}{7} )}

1 0^{3} = 1000

= \frac{5 ln ( 7 )}{ln ( \frac{1000}{7} )}

4.745 + lo g_{10} (\frac{0.146}{0.105})

3 lo g_{10} (x) + 4 lo g_{10} (x - 1)

2 [ln (x) - ln (x + 1) + ln (x - 1)]

\frac{1}{3} ln (y - 1) - \frac{1}{3} ln (y + 2)

ln (\frac{0.8}{0. 8 ^{2}})

What is (5ln(7))/(3ln(10)-ln(7)) ?
The solution to (5ln(7))/(3ln(10)-ln(7)) is (5ln(7))/(ln(1000/7))