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# AQA A-level Maths Exponentials An exponential function such as aˣ = b can be solved by rewriting it as logab = x, where a is the base of the logarithm. The logarithm can now be inputted on a calculator to solve for x. If the base of the logarithm is not written, it should be assumed to be 10. The natural exponential function is y = eˣ, where e is Euler's number. The inverse of the natural exponent is the natural logarithm, lnx. This can be used to solve equations with the two functions. All laws of indices apply when using the natural exponential function: when multiplying, the indices are added, and when dividing, the indices are subtracted. When Euler's number is raised to the power of 0, it equates to 1. Equations involving eˣ can be solved using the laws of indices and the knowledge that the natural logarithm is its inverse. # ✅

Solve 5ˣ = 3125. # ✅

Find the value of x in log₂(4x) = 4. # ✅

Calculate, to 2 decimal points, eˣ for when x = 5. # ✅

Given that 1/2 × lnx + 6 = 8, find the value of x to 3 significant figures. # ✅

Find the unknown value of y-coordinate of the point given on the diagram. Give the answer in 3 significant figures. # ✅

Simplify e⁵ × e⁶/e². # ✅

Give the following expression in simplified form: e⁵ × 15e⁴ × 2e/3e⁵. # ✅

The graph of y = 3e²ˣ × eˣ is provided. Calculate the y-coordinate of the point A to 3 significant figures. # ✅

Solve 20e³ˣ − 8 = 11e³ˣ + 19 for x. # ✅

Given that (eˣ − 8)(e⁵ˣ − 3) = 0, calculate the possible values of x.  Have you found the questions useful?