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if a^x= b^y = (ab)^(xy) prove that x+y =1

ln(a^x) = ln(b^y) = ln((ab)^(xy)) xln(a) = xyln(ab) ln(a) = yln(ab) = y(ln(a) + ln(b)) y = ln(a)/(ln(a)+ln(b)) with same analysis for ln(b^y): ln(b) = x(ln(a) + ln(b))x = ln(b)/(ln(a)+ln(b)) x + y = (ln(a) +...
SC
Answered by Scott C. • Maths tutor
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f(x)=2x+c, g(x) = cx+5, fg(x)= 6x+d, work out the value of d

Let’s call (f(x)=2x+c) equation 1, (g(x) = cx+5) equation 2 and (fg(x)= 6x+d) equation 3. Start by finding fg(x) in terms of c by substituting (equation 2) into (equation 1) to get (fg(x)= 2(cx +5) + c). You...
AM
Answered by Anna M. • Maths tutor
4214 Views

Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 – 9x)^4 giving each term in its simplest form.

(2-9x)^4 [2(1-4.5x)]^4 (2^4)(1-4.5x)^4 Using the binomial expansion formula 16[1+(4*(-4.5x))+(((4*(4-1))/(1 2))) (-4.5x)^2] 16[1-18x+121.5x^2] 16-288x+1944x^2
LJ
Answered by Lauren J. • Maths tutor
8455 Views

How to find gradient of functions

To find the gradient of a function, that has constant gradient you pick any two points. You label both the x and y co-ordinates of these two points.Then you subtract the y co-ordinates of these two points. Y...
SH
Answered by Sinan H. • Maths tutor
4362 Views

Solve the equation: x^2+x-12=0

x=-4, x=3
JH
Answered by Jordan H. • Maths tutor
3527 Views