What is 6ln(a/5)+4ln(7b) ?

The solution to 6ln(a/5)+4ln(7b) is ln((2401a^6b^4)/(15625))

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simplify 6ln(a/5)+4ln(7b)

simplify

6 ln (\frac{a}{5}) + 4 ln (7 b)

ln (\frac{2401 a ^{6} b ^{4}}{15625})

Solution steps

6 ln (\frac{a}{5}) + 4 ln (7 b)

Apply log rule:

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

6 ln (\frac{a}{5}) = ln ((\frac{a}{5})^{6})

= ln ((\frac{a}{5})^{6}) + 4 ln (7 b)

Apply log rule:

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

4 ln (7 b) = ln ((7 b)^{4})

= ln ((\frac{a}{5})^{6}) + ln ((7 b)^{4})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((\frac{a}{5})^{6}) + ln ((7 b)^{4}) = ln ((\frac{a}{5})^{6} (7 b)^{4})

= ln ((\frac{a}{5})^{6} (7 b)^{4})

Simplify

(\frac{a}{5})^{6} (7 b)^{4} : \frac{2401 a ^{6} b ^{4}}{15625}

= ln (\frac{2401 a ^{6} b ^{4}}{15625})

8 \cdot lo g_{b} (x) + 9 \cdot lo g_{b} (y) - 4 \cdot lo g_{b} (z)

ln (1 i)

ln (- 2 t)

\frac{ln ( 3.4 ) - ln ( 1.2 )}{0.01 ln ( 2 )}

- lo g_{10} (3.36 \cdot 1 0^{- 4})

What is 6ln(a/5)+4ln(7b) ?
The solution to 6ln(a/5)+4ln(7b) is ln((2401a^6b^4)/(15625))