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In this lesson, we will learn how to solve exponential equations with base e by using natural logarithms knowing that ln(e) = 1.

Q1:

Solve 3 π β 4 = 8 π₯ , giving your answer correct to three decimal places.

Q2:

Find, to the nearest thousandth, the value of π₯ such that π = 1 9 4 π₯ β 3 .

Q3:

Solve 2 = 5 π π₯ π₯ β 1 for π₯ , giving your answer to three decimal places.

Q4:

Consider the function π ( π₯ ) = 4 π β 1 2 π + 1 ο ο .

How many solutions does the equation π ( π₯ ) = β 2 have?

How many solutions does the equation π ( π₯ ) = 1 have?

How many solutions does the equation π ( π₯ ) = 4 have?

What is the range of the function π ( π₯ ) ?

Q5:

Consider the function π ( π₯ ) = 4 π β 1 3 π + 1 ο ο .

How many solutions does the equation π ( π₯ ) = β 3 2 have?

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