A curve has equation y=e2xy = e^{2x}y=e2x
At the point P P\,P on the curve, the tangent is parallel to the line with equation 9x−2y+3=09x - 2y + 3 = 09x−2y+3=0
Find the coordinates of PPP, giving your answer in the form (lnp, q)(\ln p,\, q)(lnp,q), where p p\,p and q q\,q are rational.
104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.