What is simplify-log_{10}(5.45*10^3) ?

The solution to simplify-log_{10}(5.45*10^3) is -log_{10}(5.45)-3

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simplify-log_{10}(5.45*10^3)

simplify

- lo g_{10} (5.45 \cdot 1 0^{3})

- lo g_{10} (5.45) - 3

Decimal Notation

- 3.73639 \dots

Solution steps

- lo g_{10} (5.45 \cdot 1 0^{3})

Apply log rule:

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

lo g_{10} (5.45 \cdot 1 0^{3}) = lo g_{10} (5.45) + lo g_{10} (1 0^{3})

= - (lo g_{10} (5.45) + 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} (5.45) + 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (5.45) + 3)

Distribute parentheses

= - (lo g_{10} (5.45)) - (3)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (5.45) - 3

ln \frac{( x ^{\frac{1}{3}} )}{x ^{6} 1 + x ^{2}}

9.3098 + lo g_{10} (\frac{0.0066}{0.0468})

ln (\frac{1167}{185})

ln (\frac{x ^{5}}{y ^{3}}) + ln (\frac{1}{x ^{4} y ^{2}})

What is simplify-log_{10}(5.45*10^3) ?
The solution to simplify-log_{10}(5.45*10^3) is -log_{10}(5.45)-3