What is simplify-log_{10}(4x) ?

The solution to simplify-log_{10}(4x) is -2log_{10}(2)-log_{10}(x)

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simplify-log_{10}(4x)

simplify

- lo g_{10} (4 x)

- 2 lo g_{10} (2) - lo g_{10} (x)

Solution steps

- lo g_{10} (4 x)

Apply log rule:

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

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

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

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

= - (2 lo g_{10} (2) + lo g_{10} (x))

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{10} (2) + lo g_{10} (x)) = - 2 lo g_{10} (2) - lo g_{10} (x)

= - 2 lo g_{10} (2) - lo g_{10} (x)

- 2 [ln (2 x) - ln (3)]

\frac{5 ln ( 2 )}{ln ( \frac{5}{4} )}

lo g_{10} (an t i lo g_{4} (lo g_{2} (20) - 1))

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

(x - y ln (y) + y ln (x)) d x + x (ln (y) - ln (x))

What is simplify-log_{10}(4x) ?
The solution to simplify-log_{10}(4x) is -2log_{10}(2)-log_{10}(x)