What is 4log_{10}(5)+1log_{10}(x) ?

The solution to 4log_{10}(5)+1log_{10}(x) is log_{10}(625x)

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simplify 4log_{10}(5)+1log_{10}(x)

simplify

4 lo g_{10} (5) + 1 lo g_{10} (x)

lo g_{10} (625 x)

Solution steps

4 lo g_{10} (5) + 1 \cdot lo g_{10} (x)

Apply rule:

1 \cdot a = a

1 \cdot lo g_{10} (x) = lo g_{10} (x)

= 4 lo g_{10} (5) + lo g_{10} (x)

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

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

Simplify

5^{4} x : 625 x

= lo g_{10} (625 x)

\frac{1}{7} lo g_{3} (5)

lo g_{8} (\frac{w ^{2}}{v})

\frac{1}{2} (lo g_{8} (x) + lo g_{8} (y))

ln (\frac{m}{n})

What is 4log_{10}(5)+1log_{10}(x) ?
The solution to 4log_{10}(5)+1log_{10}(x) is log_{10}(625x)