What is log_{10}(50*5^{1/2})+3log_{10}(99) ?

The solution to log_{10}(50*5^{1/2})+3log_{10}(99) is 1+log_{10}(4851495*5^{1/2})

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simplify log_{10}(50*5^{1/2})+3log_{10}(99)

simplify

lo g_{10} (50 \cdot 5^{\frac{1}{2}}) + 3 lo g_{10} (99)

1 + lo g_{10} (4851495 \cdot 5^{\frac{1}{2}})

Decimal Notation

8.03536 \dots

Solution steps

lo g_{10} (50 \cdot 5^{\frac{1}{2}}) + 3 lo g_{10} (99)

lo g_{10} (50 \cdot 5^{\frac{1}{2}}) = 1 + lo g_{10} (5) + \frac{1}{2} lo g_{10} (5)

= (1 + lo g_{10} (5) + \frac{1}{2} lo g_{10} (5)) + 3 lo g_{10} (99)

Apply rule:

(a) = a

(1 + lo g_{10} (5) + \frac{1}{2} lo g_{10} (5)) = 1 + lo g_{10} (5) + \frac{1}{2} lo g_{10} (5)

= 1 + lo g_{10} (5) + \frac{1}{2} lo g_{10} (5) + 3 lo g_{10} (99)

\frac{1}{2} lo g_{10} (5) = lo g_{10} (5^{\frac{1}{2}})

3 lo g_{10} (99) = lo g_{10} (9 9^{3})

= 1 + lo g_{10} (5) + lo g_{10} (5^{\frac{1}{2}}) + lo g_{10} (9 9^{3})

lo g_{10} (5) + lo g_{10} (5^{\frac{1}{2}}) + lo g_{10} (9 9^{3}) = lo g_{10} (4851495 \cdot 5^{\frac{1}{2}})

= 1 + lo g_{10} (4851495 \cdot 5^{\frac{1}{2}})

ln (1 5^{'} 83)

4 lo g_{3} (x) + \frac{1}{3} lo g_{3} (y) - 5 lo g_{3} (z)

lo g_{10} (b c)

lo g_{10} (2) + lo g_{10} (x) + lo g_{10} (y)

lo g_{10} (\frac{( x ^{2} )}{( y ^{4} \cdot z )})

What is log_{10}(50*5^{1/2})+3log_{10}(99) ?
The solution to log_{10}(50*5^{1/2})+3log_{10}(99) is 1+log_{10}(4851495*5^{1/2})