# j-james/math

All my math notes, now in Markdown.

View the Project on GitHub j-james/math

# Solving Non Simple Exponential Functions

## Learning Targets

You should be able to

• Solve non simple exponential functions

## 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 $x + \log_3 x = 8$