MHB Find the value of this equation

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The discussion centers on solving the equation (4)^x - 1/2y, with participants clarifying the expression's format and the meaning of the variables involved. The equation is interpreted as 4^x - (1/2)y, leading to a transformation into exponential form. Participants explain that 4^x can be rewritten as 2^(2x), facilitating further simplification. The conversation emphasizes understanding the notation and the steps to manipulate the equation correctly. Overall, the thread provides valuable insights for those struggling with similar mathematical expressions.
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My question is find the value of (4)^x-1/2y
Sorry I just joined and not sure how to use the symbols. Also I would try and show my workings out but i am stumped! Need some help
 
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mathsheadache said:
My question is find the value of (4)^x-1/2y
Sorry I just joined and not sure how to use the symbols. Also I would try and show my workings out but i am stumped! Need some help

Welcome on MHB mathsheadache!...

... usually an equation in one unknown x is written in form of equality like f(x)=0 and his solution is to find the values ​​of x that satisfy the equality...

Kind regards

$\chi$ $\sigma$
 
mathsheadache said:
My question is find the value of (4)^x-1/2y
Sorry I just joined and not sure how to use the symbols. Also I would try and show my workings out but i am stumped! Need some help

First, is it $$4^x-\frac{1}{2}y$$ or $$4^x-\frac{1}{2y}$$?

Second, are you given values for $x$ and $y$?
 
MarkFL said:
First, is it $$4^x-\frac{1}{2}y$$ or $$4^x-\frac{1}{2y}$$?

Second, are you given values for $x$ and $y$?
x and y has no values

It would be the first one, the 4 is in brackets and it would all be to the power of 4.
I hope you understand
 
$$4^{x-\frac{y}{2}} = \frac{4^x}{4^{\frac{y}{2}}} = \frac{4^x}{2^y} = \frac{2^{2x}}{2^y} = 2^{2x-y}$$

... take your pick ;)
 
skeeter said:
$$4^{x-\frac{y}{2}} = \frac{4^x}{4^{\frac{y}{2}}} = \frac{4^x}{2^y} = \frac{2^{2x}}{2^y} = 2^{2x-y}$$

... take your pick ;)

I am not sure how you got -y/2. The question would be X minus a half as a fraction then Y all to the power of (4)
 
mathsheadache said:
I am not sure how you got -y/2. The question would be X minus a half as a fraction then Y all to the power of (4)

$$\frac{1}{2}y = \frac{y}{2}$$
 
skeeter said:
$$\frac{1}{2}y = \frac{y}{2}$$

Oh wow that makes a lot more sense! So can you say Y x 1/2 would equal Y/2?
and I understand the steps until 2^2x/2Y. Where did the 2^2x come from?

Thank you
 
$$4^x = (2^2)^x = 2^{2x}$$
 
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skeeter said:
$$4^x = (2^2)^x = 2^{2x}$$

I understand now thank you!

Does anyone know this topic so I can revise furthermore?
 
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