Use the rules of exponents and logarithms to solve the equation. The logarithm of a number raised to a power is the power times the logarithm of the number. By the change-of-base formula \frac {\log (a)} {\log (b)}=\log_ {b}\left (a\right). If 2^x=100, what is the value of x using a logarithm?

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x=3.32192… What is the answer to 4^x=100 ?

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To check that x^{100} - 1 is divisible by 1000, it will suffice to check that it is divisible by 8 and 125. For each of these, you can use Euler's theorem, which will tell you that x^{p^{k-1}(p-1)} \equiv 1 \pmod {p^k} ...

x=\frac{0±\sqrt{0^{2}-4\times 4\left(-100\right)}}{2\times 4} This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

What are the solutions to the equation x^4=100 ?

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