What is (2log_{2}(7))(log_{7}(8)+log_{7}(4)) ?

The solution to (2log_{2}(7))(log_{7}(8)+log_{7}(4)) is 10

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simplify (2log_{2}(7))(log_{7}(8)+log_{7}(4))

simplify

(2 lo g_{2} (7)) (lo g_{7} (8) + lo g_{7} (4))

10

Solution steps

(2 lo g_{2} (7)) (lo g_{7} (8) + lo g_{7} (4))

lo g_{7} (8) + lo g_{7} (4) = 5 lo g_{7} (2)

= 2 lo g_{2} (7) \cdot 5 lo g_{7} (2)

Multiply the numbers:

2 \cdot 5 = 10

= 10 lo g_{2} (7) lo g_{7} (2)

Apply log rule:

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

lo g_{2} (7) = \frac{ln ( 7 )}{ln ( 2 )}

= 10 \cdot \frac{ln ( 7 )}{ln ( 2 )} lo g_{7} (2)

Apply log rule:

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

lo g_{7} (2) = \frac{ln ( 2 )}{ln ( 7 )}

= 10 \cdot \frac{ln ( 7 )}{ln ( 2 )} \cdot \frac{ln ( 2 )}{ln ( 7 )}

Cross cancel:

\frac{a}{b} \cdot \frac{b}{a} = 1

\frac{ln ( 7 )}{ln ( 2 )} \cdot \frac{ln ( 2 )}{ln ( 7 )} = 1

= 10 \cdot 1

Multiply the numbers:

10 \cdot 1 = 10

= 10

10 x^{2} - 6 = 9 x

5 x^{5} y^{2} - 80 x y^{2}

\frac{1}{3 + i}

\frac{2 ^{16}}{2 ^{4}}

t^{3} + 8

What is (2log_{2}(7))(log_{7}(8)+log_{7}(4)) ?
The solution to (2log_{2}(7))(log_{7}(8)+log_{7}(4)) is 10