What is (ln(3)+ln(32))/(ln(3)-ln(16)) ?

The solution to (ln(3)+ln(32))/(ln(3)-ln(16)) is (ln(96))/(ln(3/16))

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simplify (ln(3)+ln(32))/(ln(3)-ln(16))

simplify

\frac{ln ( 3 ) + ln ( 32 )}{ln ( 3 ) - ln ( 16 )}

\frac{ln ( 96 )}{ln ( \frac{3}{16} )}

Decimal Notation

- 2.72665 \dots

Solution steps

\frac{ln ( 3 ) + ln ( 32 )}{ln ( 3 ) - ln ( 16 )}

Apply log rule:

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

ln (3) + ln (32) = ln (3 \cdot 32)

= \frac{ln ( 3 \cdot 32 )}{ln ( 3 ) - ln ( 16 )}

Multiply the numbers:

3 \cdot 32 = 96

= \frac{ln ( 96 )}{ln ( 3 ) - ln ( 16 )}

Apply log rule:

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

ln (3) - ln (16) = ln (\frac{3}{16})

= \frac{ln ( 96 )}{ln ( \frac{3}{16} )}

- lo g_{10} (1.7 \cdot 1 0^{- 3})

4 lo g_{10} (4) - 2 lo g_{10} (x)

lo g_{4} (x z^{3})

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

- lo g_{10} (x + 6) + lo g_{10} (x - 5)

What is (ln(3)+ln(32))/(ln(3)-ln(16)) ?
The solution to (ln(3)+ln(32))/(ln(3)-ln(16)) is (ln(96))/(ln(3/16))