j-james/math

All my math notes, now in Markdown.

View the Project on GitHub j-james/math

Solving Exponential and Logs

Learning Targets

You should be able to

• Solve simple exponential and log equations

Concepts / Definitions

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 $\log x^4 = 2$