What is (ln(6)+ln(2))/(log_{10)(6)+log_{10}(2)} ?

The solution to (ln(6)+ln(2))/(log_{10)(6)+log_{10}(2)} is (ln(12))/(log_{10)(12)}

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simplify (ln(6)+ln(2))/(log_{10)(6)+log_{10}(2)}

simplify

\frac{ln ( 6 ) + ln ( 2 )}{lo g _{10} ( 6 ) + lo g _{10} ( 2 )}

\frac{ln ( 12 )}{lo g _{10} ( 12 )}

Decimal Notation

2.30258 \dots

Solution steps

\frac{ln ( 6 ) + ln ( 2 )}{lo g _{10} ( 6 ) + lo g _{10} ( 2 )}

Apply log rule:

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

ln (6) + ln (2) = ln (6 \cdot 2)

= \frac{ln ( 6 \cdot 2 )}{lo g _{10} ( 6 ) + lo g _{10} ( 2 )}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{ln ( 12 )}{lo g _{10} ( 6 ) + lo g _{10} ( 2 )}

Apply log rule:

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

lo g_{10} (6) + lo g_{10} (2) = lo g_{10} (6 \cdot 2)

= \frac{ln ( 12 )}{lo g _{10} ( 6 \cdot 2 )}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{ln ( 12 )}{lo g _{10} ( 12 )}

\frac{1}{3} lo g_{c} (x) + 4 lo g_{c} (y) - 5 lo g_{c} (x)

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ln (\frac{( e ^{x} )}{1 + e ^{x}})

lo g_{5} (6) + lo g_{5} (8) - lo g_{5} (12)

lo g_{2} (x) + lo g_{2} (y) - lo g_{2} (z)

What is (ln(6)+ln(2))/(log_{10)(6)+log_{10}(2)} ?
The solution to (ln(6)+ln(2))/(log_{10)(6)+log_{10}(2)} is (ln(12))/(log_{10)(12)}