Solving Simultaneous Equations and Understanding Exponential Properties

[3nder]

Just doing a bit of math homework and I am stuck on 2 questions

the first one is a similtanoius equation and goes like this

y = x - 1
y = x² -3

ive been trying for about half an hour and all i end up with is

y = (square root of) y - 2

im not sure if it's right, it does not look it.

the 2nd question i don't know the name of and looks like

7^2x = 49

i don't even know where to begin on that, i just have to factorise it.

thankyou in advanced

 

[rock.freak667]

y = x - 1
y = x² -3

ive been trying for about half an hour and all i end up with is

y = (square root of) y - 2

Instead of substituting for x, substitute for y instead.

the 2nd question i don't know the name of and looks like

7^2x = 49

Can you write 49 in any way that relates to 7?

 

[3nder]

for the 2nd question i know that x = 1 but i don't know how to write the proof, like in another question how would i do

4^3-x = 8^x

1st question solved thankyou rock.freak667

 

[rock.freak667]

for the 2nd question i know that x = 1 but i don't know how to write the proof, like in another question how would i do

4^3-x = 8^x

It all revolves around how you can write the base numbers. If you have a^m=aⁿ then m=n.

So if you have 36=6^2x, then you can write this as 6²=6^2x which means that 2=2x and hence x=1.

 

[xcvxcvvc]

for the 2nd question i know that x = 1 but i don't know how to write the proof, like in another question how would i do

4^3-x = 8^x

1st question solved thankyou rock.freak667

Also remember how a power to a power behaves:
$$(a^b)^c = a^{bc}$$

so:
$$(8)^x=(2^3)^x=2^{3x}$$

and

$$(4)^{3-x}=(2^2)^{3-x}=2^{6-2x}$$

edit: I misread and thought you said this problem's solution was x = 1. My bad!

 

[rock.freak667]

Also remember how a power to a power behaves:
$$(a^b)^c = a^{bc}$$

so:
$$(8)^x=(2^3)^x=2^{3x}$$

and

$$(4)^{3-x}=(2^2)^{3-x}=2^{6-2x}$$

edit: I misread and thought you said this problem's solution was x = 1. My bad!

Right so now you have

$$2^{6-2x}=2^{3x}$$

so what is x?