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Popular >

simplify log_{10}(1/(2^n))

Solution

simplify

lo g_{10} (\frac{1}{2 ^{n}})

Solution

- n lo g_{10} (2)

Solution steps

lo g_{10} (\frac{1}{2 ^{n}})

Simplify

\frac{1}{2 ^{n}} : (2^{n})^{- 1}

= lo g_{10} ((2^{n})^{- 1})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{10} ((2^{n})^{- 1}) = - 1 \cdot lo g_{10} (2^{n})

= - 1 \cdot lo g_{10} (2^{n})

Apply rule:

1 \cdot a = a

= - lo g_{10} (2^{n})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

- lo g_{10} (2^{n}) = - n lo g_{10} (2)

= - n lo g_{10} (2)

Popular Examples

simplify-log_{10}(8.3*10^{-5})simplify

- lo g_{10} (8.3 \cdot 1 0^{- 5})

simplify log_{10}(14)-log_{10}(7)simplify

lo g_{10} (14) - lo g_{10} (7)

simplify ln(3)+4ln(x)simplify

ln (3) + 4 ln (x)

simplify log_{10}((p^4+q)/(100))simplify

lo g_{10} (\frac{p ^{4} + q}{100})

simplify log_{2}((s^5)/(9t^2))simplify

lo g_{2} (\frac{s ^{5}}{9 t ^{2}})

Frequently Asked Questions (FAQ)

What is log_{10}(1/(2^n)) ?
The solution to log_{10}(1/(2^n)) is -nlog_{10}(2)