j-james/math

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All my math notes, now in Markdown.

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Solving Non Simple Exponential Functions

Learning Targets

You should be able to

Concepts / Definitions

Strategies

Equating if two terms, combine using properties, or factoring.

Note: All answers should be evaluated, unless it is irrational.

Examples

Example 1

Algebraically solve $e^{2x} - 7e^x = -12$

Example 2

Algebraically solve $\ln(x-2) + \ln(2x-3) = 2\ln x$

Example 3

Algebraically solve $\frac{2^x - 2^{-x}}{2} = 4$

Exercises

Solve the following algebraically. (Exact answer)

  1. $\log_4x + \log_4(x-3) = 1$
  2. $23^{2x} + 5e^x = 3$
  3. $\frac{e^x+e^{-x}}{2} = 4$
  4. $\ln(x-3) + \ln(x+4) - 3\ln2 = 0$
  5. $2^{2x} + 2^{x+2} = 12$
  6. $2\log(x+1) - 2\log6 < 0$
  7. $\ln x + \ln (x+2) = 4$
  8. $5^{x-2}=3^{3x+2}$
  9. $x^2e^x-4x^2=0$
  10. $\log_3(x-6) = \log_92x$
  11. $\frac{62}{1+3e^{-0.3x}} = 2$
  12. $\lvert\log_5x\rvert - \log_5 (2x+1) = 0$
  13. Use calculator to solve $x + \log_3 x = 8$