What is simplify-log_{10}(3.75*10^2) ?

The solution to simplify-log_{10}(3.75*10^2) is -log_{10}(3.75)-2

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simplify-log_{10}(3.75*10^2)

simplify

- lo g_{10} (3.75 \cdot 1 0^{2})

- lo g_{10} (3.75) - 2

Decimal Notation

- 2.57403 \dots

Solution steps

- lo g_{10} (3.75 \cdot 1 0^{2})

Apply log rule:

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

lo g_{10} (3.75 \cdot 1 0^{2}) = lo g_{10} (3.75) + lo g_{10} (1 0^{2})

= - (lo g_{10} (3.75) + lo g_{10} (1 0^{2}))

Apply log rule:

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

lo g_{10} (1 0^{2}) = 2 lo g_{10} (10)

= - (lo g_{10} (3.75) + 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (3.75) + 2)

Distribute parentheses

= - (lo g_{10} (3.75)) - (2)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (3.75) - 2

3 ln (x) - 2 ln (c)

lo g_{10} (\frac{1}{e})

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

\frac{ln ( 0.7182 ) + ln ( 0.6798 )}{2}

\frac{ln ( 3 ) - ln ( 2 )}{8}

What is simplify-log_{10}(3.75*10^2) ?
The solution to simplify-log_{10}(3.75*10^2) is -log_{10}(3.75)-2