What is simplify-log_{10}(2.7*10^{20}) ?

The solution to simplify-log_{10}(2.7*10^{20}) is -log_{10}(2.7)-20

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simplify-log_{10}(2.7*10^{20})

simplify

- lo g_{10} (2.7 \cdot 1 0^{20})

- lo g_{10} (2.7) - 20

Decimal Notation

- 20.43136 \dots

Solution steps

- lo g_{10} (2.7 \cdot 1 0^{20})

Apply log rule:

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

lo g_{10} (2.7 \cdot 1 0^{20}) = lo g_{10} (2.7) + lo g_{10} (1 0^{20})

= - (lo g_{10} (2.7) + lo g_{10} (1 0^{20}))

Apply log rule:

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

lo g_{10} (1 0^{20}) = 20 lo g_{10} (10)

= - (lo g_{10} (2.7) + 20 lo g_{10} (10))

20 lo g_{10} (10) = 20

= - (lo g_{10} (2.7) + 20)

Distribute parentheses

= - (lo g_{10} (2.7)) - (20)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (2.7) - 20

ln (\frac{9}{11})

2 ln (5) - 3 ln (2)

ln (d - L) + ln (d)

ln (\frac{1}{ln ( x )})

ln (\frac{6.61}{0.358})

What is simplify-log_{10}(2.7*10^{20}) ?
The solution to simplify-log_{10}(2.7*10^{20}) is -log_{10}(2.7)-20