j-james/math

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All my math notes, now in Markdown.

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Solving Exponential and Logs

Learning Targets

You should be able to

Concepts / Definitions

Follow the rules of SADME for one variable.

Solving Exponential

\(b^x = a\) \(\log_{b}{b^x} = \log_{b}{a}\) \(x = \log_{b}{a}\)

Solving Logarithmic

\(\log_{b}{x} = a\) \(b^{\log_{b}{x}} = b^a\) \(x = b^a\)

Example

Solve $5 + 2 \ln (x-1) = 4$

Exercises

  1. Solve $4^x-5=3$
  2. Solve $\frac 12(6)^{x+3} - 1 = 17$
  3. Solve $3^{x+4} + 2 = -7$
  4. Solve $10^{2x-3} + 4 = 21$ Exact and approximate answer using log button
  5. Solve $-5e^-x + 9 = 6$ Exact and approximate answer using $\ln$ button
  6. Solve $\log_2 x = -1$
  7. Solve $\log_5 \lvert 3x+1 \rvert = 2$
  8. Solve $15 + 2\log_2 x = 31$
  9. Solve $\log_6 (x-5) + 8 \leq 10$
  10. Solve $1 - 2\ln x = -4$
  11. Solve $\log_x 25 = 2$
  12. Solve $\log_3 (5x-1) = \log_3 (x+7)$
  13. Are the following equations equivalent, and do they produce the same solutions? Explain. $4\log x = 2$ and $\log x^4 = 2$