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toc = Literal equations =

A ** literal equation ** has coefficients and constants that are pronumerals. These pronumerals are also called **parameters**.

**Literal equations** are usually formulas used in practical applications.

Common literal equations include: //y = mx + c and// //y = ax// 2 //+ bx +// c, etc.

The solutions of literal equations are given in terms of the pronumeral rather than numerical values. In this section we will solve exponential literal equations and logarithmic literal equations.

** Example 1 **
math . \quad \text {Solve for x: }\quad Ae^{kx}=b,\quad \text{ where } k \in R\setminus \{0\} math

__Solution:__ math \\ . \qquad Ae^{kx}=b \\. \\ . \qquad e^{kx}=\frac{b}{A} \;\; \iff \;\; \log_e{\big(\frac{b}{A}\big)}=kx \\. \\ . \qquad x=\dfrac{1}{k} \log_e{ \left( \dfrac{b}{A} \right)} \quad k\in R\setminus \{0\} math

A CAS calculator can be used to solve for **//x//**. Use the ABC keyboard for the parameters but use the variable **x**.

** Example 2 **
math . \quad \text{Solve for x:} \quad \log_3p+ \log_3(x-8)=2\quad\text{ where }p > 0 math

__Solution:__ math . \qquad \log_3p+\log_3(x-8)=2 math . . ... ... Use log laws to combine left side into one log . math \\ . \qquad \log_3{p(x-8)}=2 \;\; \iff \;\; p(x-8)=3^2 \\. \\ . \qquad p(x-8)=9 \\. \\ . \qquad x-8=\dfrac{9}{p} math . . ... ... hence . math . \qquad x=\dfrac{9}{p}+8\quad\text{ where }p > 0 math Go to top of page flat

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