What is expand log_{10}((z^2)/4) ?

The solution to expand log_{10}((z^2)/4) is 2log_{10}(z)-2log_{10}(2)

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expand log_{10}((z^2)/4)

expand

lo g_{10} (\frac{z ^{2}}{4})

2 lo g_{10} (z) - 2 lo g_{10} (2)

Solution steps

lo g_{10} (\frac{z ^{2}}{4})

Apply log rule:

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

lo g_{10} (\frac{z ^{2}}{4}) = lo g_{10} (z^{2}) - lo g_{10} (4)

= lo g_{10} (z^{2}) - lo g_{10} (4)

Apply log rule:

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

lo g_{10} (z^{2}) = 2 lo g_{10} (z)

= 2 lo g_{10} (z) - lo g_{10} (4)

lo g_{10} (4) = 2 lo g_{10} (2)

= 2 lo g_{10} (z) - 2 lo g_{10} (2)

38 + 4 ln (86) - ln (9)

ln (\frac{2 + 1}{2})

(- ln ∣ 1 - 3 ∣ + 2 ln ∣ 1 - 2 ∣) + (- ln ∣ 0 - 3 ∣ + 2 ln ∣ 0 - 2 ∣)

lo g_{2} (76.8) - lo g_{2} (1.2)

4 lo g_{6} (x) - 5 lo g_{6} (y)

What is expand log_{10}((z^2)/4) ?
The solution to expand log_{10}((z^2)/4) is 2log_{10}(z)-2log_{10}(2)