What is simplify-log_{10}(1.7*10^5) ?

The solution to simplify-log_{10}(1.7*10^5) is -log_{10}(1.7)-5

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simplify-log_{10}(1.7*10^5)

simplify

- lo g_{10} (1.7 \cdot 1 0^{5})

- lo g_{10} (1.7) - 5

Decimal Notation

- 5.23044 \dots

Solution steps

- lo g_{10} (1.7 \cdot 1 0^{5})

Apply log rule:

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

lo g_{10} (1.7 \cdot 1 0^{5}) = lo g_{10} (1.7) + lo g_{10} (1 0^{5})

= - (lo g_{10} (1.7) + lo g_{10} (1 0^{5}))

Apply log rule:

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

lo g_{10} (1 0^{5}) = 5 lo g_{10} (10)

= - (lo g_{10} (1.7) + 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (1.7) + 5)

Distribute parentheses

= - (lo g_{10} (1.7)) - (5)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (1.7) - 5

(0.63) ln (\frac{443}{680})

ln (11 y)

lo g_{10} (x) + \frac{1}{5} lo g_{10} (y)

(75.3) ln (\frac{100}{30})

lo g_{4} (\frac{x ^{3} e ^{2}}{( 4 x + 1 ) ^{\frac{1}{2}}})

What is simplify-log_{10}(1.7*10^5) ?
The solution to simplify-log_{10}(1.7*10^5) is -log_{10}(1.7)-5