What is simplify-log_{10}(6.8*10^4) ?

The solution to simplify-log_{10}(6.8*10^4) is -log_{10}(6.8)-4

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simplify-log_{10}(6.8*10^4)

simplify

- lo g_{10} (6.8 \cdot 1 0^{4})

- lo g_{10} (6.8) - 4

Decimal Notation

- 4.83250 \dots

Solution steps

- lo g_{10} (6.8 \cdot 1 0^{4})

Apply log rule:

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

lo g_{10} (6.8 \cdot 1 0^{4}) = lo g_{10} (6.8) + lo g_{10} (1 0^{4})

= - (lo g_{10} (6.8) + lo g_{10} (1 0^{4}))

Apply log rule:

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

lo g_{10} (1 0^{4}) = 4 lo g_{10} (10)

= - (lo g_{10} (6.8) + 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (6.8) + 4)

Distribute parentheses

= - (lo g_{10} (6.8)) - (4)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (6.8) - 4

- ln (x) + \frac{1}{2} ln (b) - ln (c)

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What is simplify-log_{10}(6.8*10^4) ?
The solution to simplify-log_{10}(6.8*10^4) is -log_{10}(6.8)-4