Exponential And Logarithmic Equations Worksheet

Notes for 4.5 Exponential and Logarithmic Equations

Name:

(pp. 443 – 448)

Date:

Instructor:

Topics: Exponential Equations, Logarithmic Equations,

Applications

1. Exponential Equations (pp. 443 – 445)

We use the Identity Property that if x > 0, y > 0, a > 0, and a ≠ 1, then

x = y if and only if log

log

or ln x = ln y or log x = log y

(*whichever is needed as the inverse)

*This means that we can put in logs or lns on both sides that will activate the properties of logs

that bring down exponents within reach to become coefficients.

Ex. 5

= 13 (can also be worked with logs on both sides)

−

Ex.

* Use the calculator to go directly to the decimal answer, remembering to put ( ) around the

numerator and the denominator, and to close the ) after the ln or log button has opened one for you.

−

Ex.

300

*Always use ln on both sides to undo e and bring down the exponent.

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