What is log_{7}(1/7 a^3b) ?

The solution to log_{7}(1/7 a^3b) is -1+3log_{7}(a)+log_{7}(b)

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simplify log_{7}(1/7 a^3b)

simplify

lo g_{7} (\frac{1}{7} a^{3} b)

- 1 + 3 lo g_{7} (a) + lo g_{7} (b)

Solution steps

lo g_{7} (\frac{1}{7} a^{3} b)

\frac{1}{7} = 7^{- 1}

= lo g_{7} (7^{- 1} a^{3} b)

Apply log rule:

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

lo g_{7} (7^{- 1} a^{3} b) = lo g_{7} (7^{- 1}) + lo g_{7} (a^{3} b)

= lo g_{7} (7^{- 1}) + lo g_{7} (a^{3} b)

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{7} (7^{- 1}) = - 1

= - 1 + lo g_{7} (a^{3} b)

Simplify

lo g_{7} (a^{3} b) : 3 lo g_{7} (a) + lo g_{7} (b)

= - 1 + (3 lo g_{7} (a) + lo g_{7} (b))

Apply rule:

a + (b + c) = a + b + c

- 1 + (3 lo g_{7} (a) + lo g_{7} (b)) = - 1 + 3 lo g_{7} (a) + lo g_{7} (b)

= - 1 + 3 lo g_{7} (a) + lo g_{7} (b)

lo g_{10} (\frac{z ^{3} x ^{4}}{y})

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

lo g_{10} (24) - lo g_{10} (3) + lo g_{10} (16)

lo g_{2} (9) - lo g_{2} (11)

ln (\frac{e ^{x} - e ^{- x}}{e ^{2 x} ( 1 + x ^{3} )})

What is log_{7}(1/7 a^3b) ?
The solution to log_{7}(1/7 a^3b) is -1+3log_{7}(a)+log_{7}(b)