What is simplify-log_{10}(5.33x10^3) ?

The solution to simplify-log_{10}(5.33x10^3) is -log_{10}(5.33)-log_{10}(x)-3

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simplify-log_{10}(5.33x10^3)

simplify

- lo g_{10} (5.33 x 1 0^{3})

- lo g_{10} (5.33) - lo g_{10} (x) - 3

Solution steps

- lo g_{10} (5.33 x \cdot 1 0^{3})

Apply log rule:

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

lo g_{10} (5.33 x \cdot 1 0^{3}) = lo g_{10} (5.33) + lo g_{10} (x) + lo g_{10} (1 0^{3})

= - (lo g_{10} (x) + lo g_{10} (5.33) + lo g_{10} (1 0^{3}))

Apply log rule:

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

lo g_{10} (1 0^{3}) = 3 lo g_{10} (10)

= - (lo g_{10} (5.33) + lo g_{10} (x) + 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (x) + 3 + lo g_{10} (5.33))

Distribute parentheses

= - (lo g_{10} (5.33)) - (lo g_{10} (x)) - (3)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (5.33) - lo g_{10} (x) - 3

2 (ln (7) - 3 ln (2))

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ln (\frac{9 e ^{\frac{4 x}{117}}}{13})

ln (243) - ln (250)

What is simplify-log_{10}(5.33x10^3) ?
The solution to simplify-log_{10}(5.33x10^3) is -log_{10}(5.33)-log_{10}(x)-3