What is (5ln(6.25)-ln(0.4))/(6ln(6.25)-ln(0.4)) ?

The solution to (5ln(6.25)-ln(0.4))/(6ln(6.25)-ln(0.4)) is (ln(23841.85791…))/(ln(149011.61193…))

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simplify (5ln(6.25)-ln(0.4))/(6ln(6.25)-ln(0.4))

simplify

\frac{5 ln ( 6.25 ) - ln ( 0.4 )}{6 ln ( 6.25 ) - ln ( 0.4 )}

\frac{ln ( 23841.85791 \dots )}{ln ( 149011.61193 \dots )}

Decimal Notation

0.84615 \dots

Solution steps

\frac{5 ln ( 6.25 ) - ln ( 0.4 )}{6 ln ( 6.25 ) - ln ( 0.4 )}

Apply log rule:

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

5 ln (6.25) = ln (6.2 5^{5})

= \frac{ln ( 6.2 5 ^{5} ) - ln ( 0.4 )}{6 ln ( 6.25 ) - ln ( 0.4 )}

Apply log rule:

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

ln (6.2 5^{5}) - ln (0.4) = ln (\frac{6.2 5 ^{5}}{0.4})

= \frac{ln ( \frac{6.2 5 ^{5}}{0.4} )}{6 ln ( 6.25 ) - ln ( 0.4 )}

\frac{6.2 5 ^{5}}{0.4} = 23841.85791 \dots

= \frac{ln ( 23841.85791 \dots )}{6 ln ( 6.25 ) - ln ( 0.4 )}

Apply log rule:

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

6 ln (6.25) = ln (6.2 5^{6})

= \frac{ln ( 23841.85791 \dots )}{ln ( 6.2 5 ^{6} ) - ln ( 0.4 )}

Apply log rule:

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

ln (6.2 5^{6}) - ln (0.4) = ln (\frac{6.2 5 ^{6}}{0.4})

= \frac{ln ( 23841.85791 \dots )}{ln ( \frac{6.2 5 ^{6}}{0.4} )}

\frac{6.2 5 ^{6}}{0.4} = 149011.61193 \dots

= \frac{ln ( 23841.85791 \dots )}{ln ( 149011.61193 \dots )}

5 lo g_{b} (x) + 9 lo g_{b} (y) - 3 lo g_{b} (z)

\frac{25 ( ln ( - 3 ) - ln ( - 15 ) )}{ln ( \frac{2}{3} )}

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

5 ln (u) - 2 ln (6)

lo g_{4} (5) + lo g_{4} (16) + lo g_{4} (1.25)

What is (5ln(6.25)-ln(0.4))/(6ln(6.25)-ln(0.4)) ?
The solution to (5ln(6.25)-ln(0.4))/(6ln(6.25)-ln(0.4)) is (ln(23841.85791…))/(ln(149011.61193…))