What is expand log_{10}((2^4)/5) ?

The solution to expand log_{10}((2^4)/5) is 4log_{10}(2)-log_{10}(5)

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expand log_{10}((2^4)/5)

expand

lo g_{10} (\frac{2 ^{4}}{5})

4 lo g_{10} (2) - lo g_{10} (5)

Decimal Notation

0.50514 \dots

Solution steps

lo g_{10} (\frac{2 ^{4}}{5})

Apply log rule:

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

lo g_{10} (\frac{2 ^{4}}{5}) = lo g_{10} (2^{4}) - lo g_{10} (5)

= lo g_{10} (2^{4}) - lo g_{10} (5)

Apply log rule:

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

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

= 4 lo g_{10} (2) - lo g_{10} (5)

lo g_{10} (a) + \frac{1}{2} lo g_{10} (b) - 2 lo g_{10} (c)

lo g_{b} (y z^{4})

ln (y) + ln (3)

2 ln (cos^{2} (t)) + 2 ln (1 + tan^{2} (t))

What is expand log_{10}((2^4)/5) ?
The solution to expand log_{10}((2^4)/5) is 4log_{10}(2)-log_{10}(5)