What is simplify-log_{10}(1.47x10^{-150}) ?

The solution to simplify-log_{10}(1.47x10^{-150}) is -log_{10}(1.47)-log_{10}(x)+150

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simplify-log_{10}(1.47x10^{-150})

simplify

- lo g_{10} (1.47 x 1 0^{- 150})

- lo g_{10} (1.47) - lo g_{10} (x) + 150

Solution steps

- lo g_{10} (1.47 x \cdot 1 0^{- 150})

Apply log rule:

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

lo g_{10} (1.47 x \cdot 1 0^{- 150}) = lo g_{10} (1.47) + lo g_{10} (x) + lo g_{10} (1 0^{- 150})

= - (lo g_{10} (x) + lo g_{10} (1.47) + lo g_{10} (1 0^{- 150}))

Apply log rule:

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

lo g_{10} (1 0^{- 150}) = - 150 lo g_{10} (10)

= - (lo g_{10} (1.47) + lo g_{10} (x) - 150 lo g_{10} (10))

150 lo g_{10} (10) = 150

= - (lo g_{10} (x) + lo g_{10} (1.47) - 150)

Distribute parentheses

= - (lo g_{10} (1.47)) - (lo g_{10} (x)) - (- 150)

Apply minus-plus rules

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

= - lo g_{10} (1.47) - lo g_{10} (x) + 150

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What is simplify-log_{10}(1.47x10^{-150}) ?
The solution to simplify-log_{10}(1.47x10^{-150}) is -log_{10}(1.47)-log_{10}(x)+150