What is simplify-log_{10}(2.9*10^{13}) ?

The solution to simplify-log_{10}(2.9*10^{13}) is -log_{10}(2.9)-13

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simplify-log_{10}(2.9*10^{13})

simplify

- lo g_{10} (2.9 \cdot 1 0^{13})

- lo g_{10} (2.9) - 13

Decimal Notation

- 13.46239 \dots

Solution steps

- lo g_{10} (2.9 \cdot 1 0^{13})

Apply log rule:

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

lo g_{10} (2.9 \cdot 1 0^{13}) = lo g_{10} (2.9) + lo g_{10} (1 0^{13})

= - (lo g_{10} (2.9) + lo g_{10} (1 0^{13}))

Apply log rule:

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

lo g_{10} (1 0^{13}) = 13 lo g_{10} (10)

= - (lo g_{10} (2.9) + 13 lo g_{10} (10))

13 lo g_{10} (10) = 13

= - (lo g_{10} (2.9) + 13)

Distribute parentheses

= - (lo g_{10} (2.9)) - (13)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (2.9) - 13

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What is simplify-log_{10}(2.9*10^{13}) ?
The solution to simplify-log_{10}(2.9*10^{13}) is -log_{10}(2.9)-13