What is 3log_{10}(2)-log_{10}(4)+2log_{10}(5) ?

The solution to 3log_{10}(2)-log_{10}(4)+2log_{10}(5) is log_{10}(50)

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simplify 3log_{10}(2)-log_{10}(4)+2log_{10}(5)

simplify

3 lo g_{10} (2) - lo g_{10} (4) + 2 lo g_{10} (5)

lo g_{10} (50)

Decimal Notation

1.69897 \dots

Solution steps

3 lo g_{10} (2) - lo g_{10} (4) + 2 lo g_{10} (5)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= 3 lo g_{10} (2) - lo g_{10} (4) + lo g_{10} (5^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

= 3 lo g_{10} (2) + lo g_{10} (\frac{5 ^{2}}{4})

5^{2} = 25

= 3 lo g_{10} (2) + lo g_{10} (\frac{25}{4})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{10} (2^{3}) + lo g_{10} (\frac{25}{4})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (2^{3}) + lo g_{10} (\frac{25}{4}) = lo g_{10} (2^{3} \cdot \frac{25}{4})

= lo g_{10} (2^{3} \cdot \frac{25}{4})

2^{3} \cdot \frac{25}{4} = 50

= lo g_{10} (50)

lo g_{e} (\frac{a + x}{x})

\frac{ln ( 1500 ) - ln ( 1500 - 19200 )}{ln ( 1.03 )}

1.5 ln (\frac{13}{9})

2.1 \cdot ln (\frac{273}{233})

ln (\frac{1}{d y})

What is 3log_{10}(2)-log_{10}(4)+2log_{10}(5) ?
The solution to 3log_{10}(2)-log_{10}(4)+2log_{10}(5) is log_{10}(50)