What is 2log_{10}(5)-6log_{10}(3) ?

The solution to 2log_{10}(5)-6log_{10}(3) is log_{10}(25/729)

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simplify 2log_{10}(5)-6log_{10}(3)

simplify

2 lo g_{10} (5) - 6 lo g_{10} (3)

lo g_{10} (\frac{25}{729})

Decimal Notation

- 1.46478 \dots

Solution steps

2 lo g_{10} (5) - 6 lo g_{10} (3)

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

- 6 lo g_{10} (3) = - lo g_{10} (3^{6})

= lo g_{10} (5^{2}) - lo g_{10} (3^{6})

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} (3^{6}) = lo g_{10} (\frac{5 ^{2}}{3 ^{6}})

= lo g_{10} (\frac{5 ^{2}}{3 ^{6}})

\frac{5 ^{2}}{3 ^{6}} = \frac{25}{729}

= lo g_{10} (\frac{25}{729})

ln (x^{2}) - ln (x)

(\frac{1}{e})^{2} lo g_{3} (\frac{1}{e})

4 lo g_{10} (3) + 1 lo g_{10} (x)

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

lo g_{10} (x) - 5 lo g_{10} (y) + 6 lo g_{10} (z)

What is 2log_{10}(5)-6log_{10}(3) ?
The solution to 2log_{10}(5)-6log_{10}(3) is log_{10}(25/729)