Solving Natural Logs: y=(sqrt(8x^4-5))/(x-1)

• mattmannmf
In summary, the conversation discusses two options for taking the natural log of a function, y= (sqrt(8x^4-5)) / (x-1). Option 1 involves taking the natural log of both sides of the equation, while option 2 involves using the rule ln(a/b) = ln(a) - ln(b). The participants agree that both options are correct, but the second option is simpler and more commonly used.
mattmannmf
I have the following function:

y= (sqrt(8x^4-5)) / (x-1)

take the natural log of both sides:

1) ln y= ln (sqrt( 8x^4-5) - ln (x-1)

OR

2) ln y= 1/2 ln(8x^4-5) - ln (x-1)

Which one is correct?

I know when i take the natural log of a/b its ln(a)- ln(b)... but also when i take the natural log of a^q its qln(a)...does that apply in this situation also or is it just ln(a)- ln(b)?

The second would would be the correct option.

ok i thought so...thanks!

They're both correct. ln (sqrt( 8x^4-5)) = ln (8x^4 - 5)1/2 = (1/2) ln(8x^4 - 5)

Both are correct. The second is simpler and more likely to be accepted as the "correct" way.

1. How do I solve for y in the equation y=(sqrt(8x^4-5))/(x-1)?

To solve for y, you first need to isolate the square root term by multiplying both sides of the equation by (x-1). This will cancel out the denominator on the right side. Then, square both sides of the equation to eliminate the square root. You should end up with a fourth degree polynomial equation, which you can solve using methods such as factoring or the quadratic formula.

2. Can I use a calculator to solve this equation?

Yes, you can use a calculator to solve this equation. However, it is important to remember to use the order of operations and parentheses correctly to ensure accurate results.

3. What if the value of x makes the denominator equal to 0?

If the value of x makes the denominator equal to 0, the equation will be undefined. This means that the value of y is undefined for that particular value of x. You can still solve for y for other values of x.

4. Are there any restrictions on the values of x in this equation?

Yes, there are restrictions on the values of x in this equation. Since the equation contains a square root, the value inside the square root must be positive. This means that 8x^4-5 must be greater than or equal to 0. Additionally, the value of (x-1) cannot equal 0, as this would make the denominator 0. Therefore, x cannot equal 1.

5. Can this equation be solved without using the square root?

Yes, this equation can be solved without using the square root. You can use algebraic manipulations to rewrite the equation in a different form, such as factoring out x^4 and using the identity (a^2-b^2)=(a+b)(a-b). However, solving the equation using the square root may be the simplest and most straightforward approach.

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