What is 2log_{10}(5)-2log_{10}(2) ?

The solution to 2log_{10}(5)-2log_{10}(2) is log_{10}(25/4)

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simplify 2log_{10}(5)-2log_{10}(2)

simplify

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

lo g_{10} (\frac{25}{4})

Decimal Notation

0.79588 \dots

Solution steps

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

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

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

\frac{5 ^{2}}{2 ^{2}} = \frac{25}{4}

= lo g_{10} (\frac{25}{4})

ln (2 e^{3})

ln (e^{2} x)

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

ln (2 a) - ln (a)

lo g_{10} (\frac{x ^{3}}{y ^{4}})

What is 2log_{10}(5)-2log_{10}(2) ?
The solution to 2log_{10}(5)-2log_{10}(2) is log_{10}(25/4)