Linear Function of x: Simplifying ln(y) with 6.3 and 1.5 coefficients

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To express ln(y) as a linear function of x for the equation y=(6.3)(1.5)x, the correct formulation is ln(y) = x ln(1.5) + ln(6.3). This shows that ln(y) is indeed a linear function of x, as x is only raised to the first power. The initial confusion was clarified with confirmation that the approach was correct. The discussion emphasizes the importance of recognizing the linear relationship in logarithmic transformations. Understanding this concept is essential for simplifying expressions involving exponential functions.
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Hey guys, I'm absolutely stuck on how to do this. I really don't even know where to begin. A push in the right direction would be great! Here's the problem:

Let y=(6.3)(1.5)x. Write ln(y) as a linear function of x.

I came up with this, bu I don't think it's right:

ln(y)= x ln(1.5) + ln(6.3)

Is that what they're looking for? Or am I way off?
 
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Yes, that looks good. You can see that ln(y) is a linear function of x, because x appears only raised to the first power.
 
Great, thanks for the confirmation!
 
The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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