What is log_{7}(2*6)+log_{7}(3) ?

The solution to log_{7}(2*6)+log_{7}(3) is 2log_{7}(6)

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simplify log_{7}(2*6)+log_{7}(3)

simplify

lo g_{7} (2 \cdot 6) + lo g_{7} (3)

2 lo g_{7} (6)

Decimal Notation

1.84156 \dots

Solution steps

lo g_{7} (2 \cdot 6) + lo g_{7} (3)

2 \cdot 6 = 12

= lo g_{7} (12) + lo g_{7} (3)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{7} (12) + lo g_{7} (3) = lo g_{7} (12 \cdot 3)

= lo g_{7} (12 \cdot 3)

Multiply the numbers:

12 \cdot 3 = 36

= lo g_{7} (36)

Factor the number:

36 = 6^{2}

= lo g_{7} (6^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{7} (6^{2}) = 2 lo g_{7} (6)

= 2 lo g_{7} (6)

- \frac{1}{14} ln ∣ 3 x - 1 ∣ - 3 ln ∣ 3 - 2 ∣ + \frac{32}{7} ln ∣ 3 + 3 ∣

lo g_{b} (z^{6} x)

\frac{2 ln ( 3 )}{ln ( 7 )} + 6

ln (\frac{27}{2})

What is log_{7}(2*6)+log_{7}(3) ?
The solution to log_{7}(2*6)+log_{7}(3) is 2log_{7}(6)