Algebra 2

[conrad hoffmann]

How do you graph y=log (sub #9) 5(x+2)?

 

[Gene]

log₉(5(x+2))=
ln(5x+10)/ln(9)=
log(5x+10)/log(9)

 

[soroban]

Hello, Conrad!

Graph: \(\displaystyle \,y\:=\:\log_95(x\,+\,2)\)

I believe you're expected to use "transformations".

The basic log graph, \(\displaystyle y\:=\:\log_b(x),\;b\,>\,1\,\), looks like this:

      |                *
      |           *
      |       *
    --+----*-----------
      |  * 1
      | *
      |
      |*
      |

\(\displaystyle y\:=\:\log_9(x\,+\,2)\) is the same graph, moved 5 units to the left.


Since \(\displaystyle y\:=\:\log_95(x\,+\,2)\;=\;\log_9(5)\,+\,\log_9(x\,+\,2)\)

\(\displaystyle \;\;\)the previous graph is moved up \(\displaystyle \log_9(5)\) units.