Mathematics, 17.08.2020 14:01 lakiprincess

Logx - logx-1^2=2log(x-1)

Answers: 3

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Answer from: caleb768

x is approximately 2.220744

Step-by-step explanation:

This can be simplified a little using properties of logarithms, and then solve it by graphing:

$log(x)-log(x-1)^2=2\,log(x-1)\\log(x)-2\,log(x-1)=2\,log(x-1)\\log(x)=4\,log(x-1)$

So we use a graphing tool to find the intersection point of the graph of log(x) , and the graph of $4\,log(x-1)$

Please see attached image for the graph and solution.

The value of x is approximately 2.220744

Answer from: lolirdc

x = 2.32011574011

Step-by-step explanation:

The problem with your original equation is that it is a long way of saying ...

log(x) -log(x) -1 = 2log(x-1)

0 -1 = 2log(x-1)

which has the solution ...

-1/2 = log(x -1)

1/√10 = x -1

x = 1 + 1/√10 ≈ 1.3162278

We have asked for clarification, and what we got was ...

$\log{(x)}-\log{(x-1^2)}=2\log{(x-1)}$

which, again, is a long way of saying ...

$\log{(x)}-\log{(x-1)}=2\log{(x-1)}$

The other reasonable interpretation of your 'clarified' equation is ...

$\log{(x)}-\log{((x-1)^2)}=2\log{(x-1)}$

which you already have an answer to. You have declared that a "misconception."

So, we are left with the interpretation that the equation you want a solution to is ...

$\log{(x)}-\log{(x-1)}=2\log{(x-1)}$

_____

When solving these graphically, I like to write the equation as a function whose zero(s) we're trying to find. For this, when we subtract the right side, we get ...

$f(x)=\log{(x)}-3\log{(x-1)}$

A graphing calculator shows that f(x) = 0 when ...

x ≈ 2.32011574011

If you don't like my interpretation, check out the second attachment. It has your x-1² as the argument of the middle term. You can see that the calculator interpreted that the same way I did (as required by the order of operations).

Answer from: Quest

The answer would be 24mm
What is the length of the missing leg in this right triangle ?

Answer from: Quest

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

$\tan\left(x\right)=\frac{\left[altitude\right]}{\left[base\right]}=\frac{p}{r}$

$\tan\left(x\right)=\frac{p}{r}$

$\frac{p}{r}=tan(x)$

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

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