What is expand log_{10}(y^6x) ?

The solution to expand log_{10}(y^6x) is 6log_{10}(y)+log_{10}(x)

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expand log_{10}(y^6x)

expand

lo g_{10} (y^{6} x)

6 lo g_{10} (y) + lo g_{10} (x)

Solution steps

lo g_{10} (y^{6} x)

Apply log rule:

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

lo g_{10} (y^{6} x) = lo g_{10} (y^{6}) + lo g_{10} (x)

= lo g_{10} (y^{6}) + lo g_{10} (x)

Apply log rule:

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

lo g_{10} (y^{6}) = 6 lo g_{10} (y)

= 6 lo g_{10} (y) + lo g_{10} (x)

- 0.9 lo g_{2} (0.9) - 0.1 \cdot lo g_{2} (0.05)

ln (\frac{6561}{64}) - \frac{9}{4} + 3 ln (3) - 12 ln (2) + 3

- ln (2 x - 2) + ln (2 x - 4)

4 ln (2) - 5 ln (3)

10 \cdot lo g_{10} (1 0^{\frac{a}{10}} - 1 0^{\frac{b}{10}})

What is expand log_{10}(y^6x) ?
The solution to expand log_{10}(y^6x) is 6log_{10}(y)+log_{10}(x)