What is expand log_{10}(y^9x) ?

The solution to expand log_{10}(y^9x) is 9log_{10}(y)+log_{10}(x)

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expand log_{10}(y^9x)

expand

lo g_{10} (y^{9} x)

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

Solution steps

lo g_{10} (y^{9} x)

Apply log rule:

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

lo g_{10} (y^{9} x) = lo g_{10} (y^{9}) + lo g_{10} (x)

= lo g_{10} (y^{9}) + lo g_{10} (x)

Apply log rule:

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

lo g_{10} (y^{9}) = 9 lo g_{10} (y)

= 9 lo g_{10} (y) + lo g_{10} (x)

- \frac{1}{100} \cdot ln (\frac{0.01}{0.184})

ln (\frac{220}{450})

ln (t - 12) - ln (t - 11) + ln (2)

ln (\frac{x}{( x + 1 ) ^{9} ( x + 8 ) ^{4}})

3 ln (x + 6) - 7 ln (x)

What is expand log_{10}(y^9x) ?
The solution to expand log_{10}(y^9x) is 9log_{10}(y)+log_{10}(x)