What is sqrt(4log_{10)(2)+log^2_{10}(5)} ?

The solution to sqrt(4log_{10)(2)+log^2_{10}(5)} is sqrt(log_{10)(80)}

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simplify sqrt(4log_{10)(2)+log^2_{10}(5)}

simplify

4 lo g_{10} (2) + lo g_{10}^{2} (5)

lo g_{10} (80)

Decimal Notation

1.37952 \dots

Solution steps

4 lo g_{10} (2) + lo g_{10}^{2} (5)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

lo g_{10} (2^{4}) + lo g_{10}^{2} (5) = lo g_{10} (2^{4} \cdot 5)

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

2^{4} \cdot 5 = 80

= lo g_{10} (80)

- lo g_{10} (6 \cdot 1 0^{- 10})

\frac{1}{2} ln (5 x^{2}) - \frac{1}{2} ln (2 x^{2})

- 6 (ln (3) - ln (2)) + \frac{7}{2} - 6 ln (2) + \frac{15}{2}

1.6 ln (\frac{2.242}{1.2})

- ln (9.6 - 3) + 2 ln (9.6 - 2)

What is sqrt(4log_{10)(2)+log^2_{10}(5)} ?
The solution to sqrt(4log_{10)(2)+log^2_{10}(5)} is sqrt(log_{10)(80)}