What is expand log_{10}((1/4)_{2})+1 ?

The solution to expand log_{10}((1/4)_{2})+1 is -2log_{10}(2)+1

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expand log_{10}((1/4)_{2})+1

expand

lo g_{10} ((\frac{1}{4})_{2}) + 1

- 2 lo g_{10} (2) + 1

Decimal Notation

0.39794 \dots

Solution steps

lo g_{10} ((\frac{1}{4})_{2}) + 1

Apply log rule:

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

lo g_{10} ((\frac{1}{4})_{2}) = lo g_{10} (\frac{1}{4})

= lo g_{10} (\frac{1}{4}) + 1

Apply log rule:

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

lo g_{10} (\frac{1}{4}) = lo g_{10} (1) - lo g_{10} (4)

= lo g_{10} (1) - lo g_{10} (4) + 1

Apply log rule:

lo g_{a} (1) = 0

= 0 - lo g_{10} (4) + 1

Add the numbers:

0 + 1 = 1

= - lo g_{10} (4) + 1

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

= - 2 lo g_{10} (2) + 1

ln (8) - ln (e^{y})

ln (\frac{343}{293})

ln (\frac{∣ Bl - E ∣}{∣ E ∣})

lo g_{2} (0.7) \cdot 0.7 + lo g_{2} (0.3) \cdot 0.3

- ln (\frac{( x - y )}{x})

What is expand log_{10}((1/4)_{2})+1 ?
The solution to expand log_{10}((1/4)_{2})+1 is -2log_{10}(2)+1