3.2a Lesson on Logarithms

Logarithms let you solve for exponents

Any time you don't know an exponent, you will put a "log" in your problem

• All calculators are programmed with bases of 10 to save space. We have a base of 3

• Change of base formula log (12)/ log (3)

• Uses NORMAL LOG aka log base 10 with both

• If there is no base written on a logarithm then it is a base 10 (because of scientific notation)

Multiple Choice

How would we figure out x for

$$5^x\ =\ 39$$  ?

• $$\log_{39}5\ =\ x$$  

• $$\log_539=x$$  

• $$\log_x39\ =\ 5$$  

• $$\log_5x\ =\ 39$$  

Multiple Choice

How do you put

$$\log_539$$  in a calculator?

• $$\frac{\log\ 5}{\log\ 39}$$  

• $$\log\ \left(\frac{39}{5}\right)$$  

• $$\log\ \left(\frac{5}{39}\right)$$  

• $$\frac{\log\ 39}{\log\ 5}$$  

Multiple Choice

How do you solve

$$72\ =\ 6^x$$  

• $$\log_6x\ =\ 72$$  

• $$\log_{72}6\ =\ x$$  

• $$\log_672\ =\ x$$  

• $$\log_x72\ =\ 6$$  

Multiple Choice

How do you put

$$\log_672$$  in a calculator?

• $$\frac{\log\ 72}{\log\ 6}$$  

• $$\log\ \left(\frac{72}{6}\right)$$  

• $$\log\ \left(\frac{6}{72}\right)$$  

• $$\frac{\log\ 6}{\log\ 72}$$