What is expand log_{7}(7x^9y^8) ?

The solution to expand log_{7}(7x^9y^8) is 1+9log_{7}(x)+8log_{7}(y)

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expand log_{7}(7x^9y^8)

expand

lo g_{7} (7 x^{9} y^{8})

1 + 9 lo g_{7} (x) + 8 lo g_{7} (y)

Solution steps

lo g_{7} (7 x^{9} y^{8})

Apply log rule:

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

lo g_{7} (7 x^{9} y^{8}) = lo g_{7} (7) + lo g_{7} (x^{9}) + lo g_{7} (y^{8})

= lo g_{7} (7) + lo g_{7} (x^{9}) + lo g_{7} (y^{8})

Apply log rule:

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

lo g_{7} (x^{9}) = 9 lo g_{7} (x)

= lo g_{7} (7) + 9 lo g_{7} (x) + lo g_{7} (y^{8})

Apply log rule:

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

lo g_{7} (y^{8}) = 8 lo g_{7} (y)

= lo g_{7} (7) + 9 lo g_{7} (x) + 8 lo g_{7} (y)

Apply log rule:

lo g_{a} (a) = 1

= 1 + 9 lo g_{7} (x) + 8 lo g_{7} (y)

- lo g_{10} (6.9 \cdot 1 0^{- 5})

ln (\frac{4}{245})

+ 2 ln (x) - 2 ln (y)

lo g_{2} (\frac{c ^{3}}{d})

What is expand log_{7}(7x^9y^8) ?
The solution to expand log_{7}(7x^9y^8) is 1+9log_{7}(x)+8log_{7}(y)