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- Exponential and Logarithmic functions

Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

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Get Started Now- Lesson: 13:21
- Lesson: 2a1:04
- Lesson: 2b1:09
- Lesson: 2c1:21
- Lesson: 2d1:41
- Lesson: 3a3:11
- Lesson: 3b6:47

Basic Concepts: Converting from logarithmic form to exponential form, Evaluating logarithms without a calculator, Common logarithms

Related Concepts: Logarithmic scale: Richter scale (earthquake), Logarithmic scale: pH scale, Logarithmic scale: dB scale

• change-of-base rule:$\log_ba = \frac{\log_xa}{\log_xb} = \frac{\log a}{\log b}$

• common logarithms:log with base $``10"$example: $\log3 = \log_{10}3$

example: $\log x = \log_{10}x$

• common logarithms:log with base $``10"$example: $\log3 = \log_{10}3$

example: $\log x = \log_{10}x$

- 1.How to apply $``$change-of-base rule$"$

Express $\log_53$ in three different ways. - 2.Using a calculator, evaluate the following logarithms

by applying $``$ change-of-base rule$":$a)$\log_53$b)$\log_7\sqrt{416}$c)$\log_2\frac{7}{25}$d)6$\log_4999$ - 3.Using a calculator, solve for $x$ to the nearest hundredth.a)$\log_6x = log_7 8$b)$\log_{23}5 = log_x\sqrt{0.104}$

6.

Exponential and Logarithmic functions

6.1

Converting from logarithmic form to exponential form

6.2

Evaluating logarithms without calculator

6.3

Common logarithms

6.4

Evaluating logarithms using change-of-base formula

6.5

Converting from exponential form to logarithmic form

6.6

Product rule of logarithms

6.7

Quotient rule of logarithms

6.8

Combining product rule and quotient rule in logarithms

6.9

Solving logarithmic equations

6.10

Evaluating logarithms using logarithm rules

6.11

Continuous growth and decay

6.12

Finance: Compound interest

6.13

Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$

6.14

Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$

6.15

Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$

6.16

Exponents: Negative exponents

6.17

Exponents: Zero exponent: $a^0 = 1$

6.18

Exponents: Rational exponents

6.19

Graphing exponential functions

6.20

Graphing transformations of exponential functions

6.21

Finding an exponential function given its graph

6.22

Logarithmic scale: Richter scale (earthquake)

6.23

Logarithmic scale: pH scale

6.24

Logarithmic scale: dB scale

6.25

Finance: Future value and present value

We have over 830 practice questions in Precalculus for you to master.

Get Started Now6.1

Converting from logarithmic form to exponential form

6.2

Evaluating logarithms without calculator

6.3

Common logarithms

6.4

Evaluating logarithms using change-of-base formula

6.5

Converting from exponential form to logarithmic form

6.6

Product rule of logarithms

6.11

Continuous growth and decay

6.12

Finance: Compound interest

6.13

Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$

6.14

Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$

6.15

Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$

6.16

Exponents: Negative exponents

6.18

Exponents: Rational exponents

6.22

Logarithmic scale: Richter scale (earthquake)

6.23

Logarithmic scale: pH scale

6.24

Logarithmic scale: dB scale

6.25

Finance: Future value and present value