What is log_{10}(5^3)-log_{10}(25^2) ?

The solution to log_{10}(5^3)-log_{10}(25^2) is -log_{10}(5)

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simplify log_{10}(5^3)-log_{10}(25^2)

simplify

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

- lo g_{10} (5)

Decimal Notation

- 0.69897 \dots

Solution steps

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (5^{3}) = 3 lo g_{10} (5)

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

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

= 3 lo g_{10} (5) - 4 lo g_{10} (5)

Add similar elements:

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

= - lo g_{10} (5)

\frac{x}{2} + \frac{x}{5}

\frac{6 b ^{2} ( a + 2 b ^{2} ) ( a - 2 b ^{2} )}{32 a b ^{5} - 8 a ^{3} b}

\frac{6 ^{8} 4 ^{9} m}{6 ^{6} 4 ^{8} m}

8 x^{3} - 125 t^{3}

\frac{4}{x ^{2} - 3 x + 4} + \frac{3}{x ^{2} - 16} - \frac{7}{x ^{2} + 5 x + 4}

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