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Popular >

simplify 10^{log_{100}(x)}

Solution

simplify

1 0^{l o g_{100} (x)}

Solution

x

Solution steps

1 0^{l o g_{100} (x)}

Factor the number:

100 = 1 0^{2}

= 1 0^{l o g_{1 0^{2}} (x)}

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{1 0^{2}} (x) = \frac{1}{2} lo g_{10} (x)

= 1 0^{\frac{1}{2} l o g_{10} (x)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}, a \geq 0

1 0^{\frac{1}{2} l o g_{10} (x)} = (1 0^{l o g_{10} (x)})^{\frac{1}{2}}

= (1 0^{l o g_{10} (x)})^{\frac{1}{2}}

Apply log rule:

a^{l o g_{a} (b)} = b

1 0^{l o g_{10} (x)} = x

= x^{\frac{1}{2}}

Apply exponent rule:

a^{\frac{1}{2}} = a

x^{\frac{1}{2}} = x

= x

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Frequently Asked Questions (FAQ)

What is 10^{log_{100}(x)} ?
The solution to 10^{log_{100}(x)} is sqrt(x)