Evaluating Logs using Exponents and Using Log Laws to Evaluate Values

Today we looked at the similarities between exponent forms and Logarithmic fomrs of values of numbers.

We saw that for y = b^x we can rearrange this exponential form to a Logarithmic form such that

y = b^x < -> logbx = y

We can use this to evaluate expontial values

It is easy to see that 10^x = 1000 because 10^3 = 1000, so 10^x = 10^3, and dropping bases x = 3

But what if 10^x = 81?  This means: 10 to the power of what will result in 81?

We can see that 

10^1 = 10 and 10^2 = 100

81 lies between 10 and 100 (closer to 100) therefore the exponent of 10 must be between 1 & 2 (and closer to 2)

81 = 10^x -> changing exponents to log form x = log 1081,  x = 1.908.

This means 10^1.908  = 81

We summarized the steps to be:

• REARRANGE Log form to Exponential form
• re-write exponential forms to have the SAME BASE
• Use EXPONENT LAWS if necessary
• DROP BASES due to equivalent forms of exponents
• SOLVE

We also discovered the laws that apply to log functions are similar to exponent laws.

See the notes below.

• Apply LOG LAWS where you can to create a single Log function
• REARRANGE Log form to Exponential form
• re-write exponential forms to have the SAME BASE
• Use EXPONENT LAWS if necessary
• DROP BASES due to equivalent forms of exponents
• SOLVE

HW - see calendar from the first Post for today's HW.