Calculate the power, given all other numbers in an equation

Question

$$100 = 200(2)^x$$

Given all numbers in the equation, how do I find $x$?

Answer 1

If you divide both sides by 200 you end up with $$ \frac12 = 2^x $$ At this point you have to remember that $\frac12$ is exactly how $2^{-1}$ is defined, such that $x=-1$ is a solution.

Answer 2

Hint : Take the logarithm on both sides and use $log(a^n)=n\ log(a)$ and $log(ab)=log(a)+log(b)$

Answer 3

cancalling with $100$ we get $$2^{-1}=2^x$$ thus we get $$x=-1$$

Answer 4

Notice, we have $$100=200\cdot 2^x$$ Diving both the sides by $100$ we get $$\frac{100}{100}=\frac{200}{100}\cdot 2^x$$

$$1=2\cdot2^x$$ $$1=2^{x+1}$$ $$2^0=2^{x+1}$$ Comparing powers on both the sides, we get $$x+1=0\iff x=-1$$