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Ln(3x-7)=5 Remove logs from both sides 3x-7=e⁵Rearrange to make x the subject3x=e⁵+7x=e⁵+7 3

x = 3, y = 2

First, we need to factorise the denominator and therefore we use this formula: x_1,2 =[ -b + sqrt(b² -4 a c) ]/ (2a). You obtain two roots, x = 2 and x=3 and the integration is simpli...

x² - 8x + 12 = 0 (x - 4)² - 16 + 12 = 0 (x - 4)² - 4 = 0 (x - 4)² = 4 x - 4 = +- 2 x = 6 x = 2

a) First differentiate f(x) using standard polynomial derivative rules which gives, df/dx=-3x^2+4x+3. The derivative function gives the gradient of f for any value of x. Turning points occur when the grad...