What is (ln(u^2)-ln(u)+ln(sqrt(u)))/(ln(u^3)) ?

The solution to (ln(u^2)-ln(u)+ln(sqrt(u)))/(ln(u^3)) is (ln(usqrt(u)))/(ln(u^3))

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simplify (ln(u^2)-ln(u)+ln(sqrt(u)))/(ln(u^3))

simplify

\frac{ln ( u ^{2} ) - ln ( u ) + ln ( u )}{ln ( u ^{3} )}

\frac{ln ( u u )}{ln ( u ^{3} )}

Solution steps

\frac{ln ( u ^{2} ) - ln ( u ) + ln ( u )}{ln ( u ^{3} )}

Apply log rule:

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

ln (u^{2}) - ln (u) = ln (\frac{u ^{2}}{u})

= \frac{ln ( \frac{u ^{2}}{u} ) + ln ( u )}{ln ( u ^{3} )}

Cancel the common factor:

u

= \frac{ln ( u ) + ln ( u )}{ln ( u ^{3} )}

Apply log rule:

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

ln (u) + ln (u) = ln (u u)

= \frac{ln ( u u )}{ln ( u ^{3} )}

ln (\frac{x ^{4} + 1 - x ^{2}}{x ^{4} + 1 + x ^{2}})

lo g_{\frac{4}{3}} (- 3 x) + 6

- lo g_{10} (2.07 \cdot 1 0^{- 6})

\frac{7}{2} lo g_{10} (a) + 4 lo g_{10} (b)

2 lo g_{a} (x) - lo g_{a} (x - 1) - lo g_{a} (x - 2)

What is (ln(u^2)-ln(u)+ln(sqrt(u)))/(ln(u^3)) ?
The solution to (ln(u^2)-ln(u)+ln(sqrt(u)))/(ln(u^3)) is (ln(usqrt(u)))/(ln(u^3))