What is 9/(3ln(7)-3ln(4))-4 ?

The solution to 9/(3ln(7)-3ln(4))-4 is 9/(ln(343/64))-4

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simplify 9/(3ln(7)-3ln(4))-4

simplify

\frac{9}{3 ln ( 7 ) - 3 ln ( 4 )} - 4

\frac{9}{ln ( \frac{343}{64} )} - 4

Decimal Notation

1.36082 \dots

Solution steps

\frac{9}{3 ln ( 7 ) - 3 ln ( 4 )} - 4

Apply log rule:

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

3 ln (7) = ln (7^{3})

= \frac{9}{ln ( 7 ^{3} ) - 3 ln ( 4 )} - 4

Apply log rule:

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

3 ln (4) = ln (4^{3})

= \frac{9}{ln ( 7 ^{3} ) - ln ( 4 ^{3} )} - 4

Apply log rule:

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

ln (7^{3}) - ln (4^{3}) = ln (\frac{7 ^{3}}{4 ^{3}})

= \frac{9}{ln ( \frac{7 ^{3}}{4 ^{3}} )} - 4

\frac{7 ^{3}}{4 ^{3}} = \frac{343}{64}

= \frac{9}{ln ( \frac{343}{64} )} - 4

ln (3) - ln (- 5)

- 50 ln (300) + 50 ln (450)

\frac{ln ( x )}{ln ( y ) - ln ( x )}

- ln (\frac{0.5}{ln ( 2 )})

ln (\frac{9}{6})

What is 9/(3ln(7)-3ln(4))-4 ?
The solution to 9/(3ln(7)-3ln(4))-4 is 9/(ln(343/64))-4