Which of the following pairs are equivalent statements?

Question

Which of the following pairs are equivalent statements?

http://assets.apexlearning.com/Math/200706/19/8166cc8c-9a7a-4aea-a46c-c112215e171b.gif    and http://assets.apexlearning.com/Math/200706/19/64161673-ed44-4b47-b1f9-12e92e49bcc6.gif

http://assets.apexlearning.com/Math/200706/19/ed5eac43-ec79-4850-ab05-e80903f66cd6.gif     and http://assets.apexlearning.com/Math/200706/19/64161673-ed44-4b47-b1f9-12e92e49bcc6.gif

http://assets.apexlearning.com/Math/200706/19/6a406007-bcc0-4bef-bf88-9f0dee295fca.gif        and http://assets.apexlearning.com/Math/200706/19/64161673-ed44-4b47-b1f9-12e92e49bcc6.gif

http://assets.apexlearning.com/Math/200706/19/635dd97d-fa73-48ce-bfd4-cdb8ef530d86.gif       and http://assets.apexlearning.com/Math/200706/19/64161673-ed44-4b47-b1f9-12e92e49bcc6.gif

Answer 1

When it comes to log functions there is a rule that log_a(b)=x

is equal to a^x = b. This is a rule that we have to memorize however, it is because log functions and exponential functions are inverses(opposites) of one another. I am sure there is a more extensive proof on why this is the case. You're welcome to research this. Moreover, using this rule you should be able to better identify which expressions are equivalents. I hope this helps.