What is simplify-log_{10}(4.6*10^7) ?

The solution to simplify-log_{10}(4.6*10^7) is -log_{10}(4.6)-7

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simplify-log_{10}(4.6*10^7)

simplify

- lo g_{10} (4.6 \cdot 1 0^{7})

- lo g_{10} (4.6) - 7

Decimal Notation

- 7.66275 \dots

Solution steps

- lo g_{10} (4.6 \cdot 1 0^{7})

Apply log rule:

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

lo g_{10} (4.6 \cdot 1 0^{7}) = lo g_{10} (4.6) + lo g_{10} (1 0^{7})

= - (lo g_{10} (4.6) + lo g_{10} (1 0^{7}))

Apply log rule:

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

lo g_{10} (1 0^{7}) = 7 lo g_{10} (10)

= - (lo g_{10} (4.6) + 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (4.6) + 7)

Distribute parentheses

= - (lo g_{10} (4.6)) - (7)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (4.6) - 7

3 (ln (8) - ln (4))

2 ln (ln (x)) - ln (ln (x^{2}) + 1)

ln (\frac{e ^{\frac{0.8}{x}} - 1}{e ^{\frac{0.4}{x}} - 1})

8 ln 2 + 4 - 4 + 2 ln 2 + 4 + 1

lo g_{10} (4 5^{\circ} 1 2^{\circ} 9^{\circ})

What is simplify-log_{10}(4.6*10^7) ?
The solution to simplify-log_{10}(4.6*10^7) is -log_{10}(4.6)-7