What is simplify-log_{10}(1.24*10^4) ?

The solution to simplify-log_{10}(1.24*10^4) is -log_{10}(1.24)-4

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simplify-log_{10}(1.24*10^4)

simplify

- lo g_{10} (1.24 \cdot 1 0^{4})

- lo g_{10} (1.24) - 4

Decimal Notation

- 4.09342 \dots

Solution steps

- lo g_{10} (1.24 \cdot 1 0^{4})

Apply log rule:

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

lo g_{10} (1.24 \cdot 1 0^{4}) = lo g_{10} (1.24) + lo g_{10} (1 0^{4})

= - (lo g_{10} (1.24) + lo g_{10} (1 0^{4}))

Apply log rule:

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

lo g_{10} (1 0^{4}) = 4 lo g_{10} (10)

= - (lo g_{10} (1.24) + 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (1.24) + 4)

Distribute parentheses

= - (lo g_{10} (1.24)) - (4)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (1.24) - 4

ln (x) + ln (y) - 2 x - 2 y + 2

4.76 + lo g_{10} (\frac{0.5}{3})

ln (\frac{302.12}{398})

ln (x - 2) + ln (x + 5)

ln (3.6 \cdot 1 0^{13})

What is simplify-log_{10}(1.24*10^4) ?
The solution to simplify-log_{10}(1.24*10^4) is -log_{10}(1.24)-4