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 $x$?

yes. I couldn't figure out the formatting, so I included a link to the image of my euqation — HaloMediaz, Aug 22 '15 at 19:36
Divide each side by $200$. This will make $x$ a bit more isolated, which is almost always a good thing. Reduce the fraction you get on the left-hand side. What do you get then? — Arthur, Aug 22 '15 at 19:37
Try to factorise both left hand side and right hand side then compare the powers with same base. — User23, Aug 22 '15 at 19:40
@HaloMediaz: Arthur's advice was not to carry out the division in decimal (which would produce 0.5), but merely to reduce the fraction, giving $\frac12$. So you get $\frac12=2^x$. Does that remind you of anything? — hmakholm left over Monica, Aug 22 '15 at 19:40
@HenningMakholm I can't take the square root of x to both sides get rid of the x, which is my problem. — HaloMediaz, Aug 22 '15 at 19:44
@HaloMediaz: See http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference for a tutorial in formatting formulas. $100=200 \cdot 2^x$ produces $100=200\cdot2^x$ and $.5=2^x$ produces $.5=2^x$. — hmakholm left over Monica, Aug 22 '15 at 19:56

score 0 · Answer 1 · answered Aug 22 '15 at 19:37

0

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

answered Aug 22 '15 at 19:37

Peter

84,454

If you divide by $200$ first, you do not need the second equation. – Peter Aug 22 '15 at 19:39
But he'll need to evaluate $\log_2\frac12$, that is, to solve the equation $\frac12=2^y$ for $y$, which is exactly the problem he's trying to solve in the first place! – hmakholm left over Monica Aug 22 '15 at 19:42
My hint leads him to $log(\frac{1}{2})=y\ log(2)$. The rest should be easy. It does not even matter, if he uses $log_{10}$ or ln, unless he uses two DIFFERENT logarithms. – Peter Aug 22 '15 at 19:44

score 0 · Answer 2 · answered Aug 22 '15 at 19:39

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

answered Aug 22 '15 at 19:39

Dr. Sonnhard Graubner

95,283

how did you get -1? – HaloMediaz Aug 22 '15 at 19:41

score 0 · Accepted Answer · answered Aug 22 '15 at 19:45

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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.

answered Aug 22 '15 at 19:45

hmakholm left over Monica

286,031

ok. I got it thanks. – HaloMediaz Aug 22 '15 at 19:48

score 0 · Answer 4 · answered Aug 22 '15 at 20:18

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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 $$x+1=0\iff x=-1$$

answered Aug 22 '15 at 20:18

Harish Chandra Rajpoot

37,450

Calculate the power, given all other numbers in an equation

4 Answers4