What is simplify-log_{10}(7.2*10^{-7}) ?

The solution to simplify-log_{10}(7.2*10^{-7}) is -log_{10}(7.2)+7

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simplify-log_{10}(7.2*10^{-7})

simplify

- lo g_{10} (7.2 \cdot 1 0^{- 7})

- lo g_{10} (7.2) + 7

Decimal Notation

6.14266 \dots

Solution steps

- lo g_{10} (7.2 \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (7.2 \cdot 1 0^{- 7}) = lo g_{10} (7.2) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (7.2) + 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} (7.2) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (7.2) - 7)

Distribute parentheses

= - (lo g_{10} (7.2)) - (- 7)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - lo g_{10} (7.2) + 7

3 ln (2) + \frac{1}{3} ln (8) - \frac{1}{2} ln (25)

2 ln (t) + 5 ln (z) - ln (t)

lo g_{10} (\frac{85347 x ^{15274}}{125386})

- lo g_{10} (1.74 \times 1 0^{- 5})

lo g_{9} (6 x^{3} y^{5} z)

What is simplify-log_{10}(7.2*10^{-7}) ?
The solution to simplify-log_{10}(7.2*10^{-7}) is -log_{10}(7.2)+7