How do you graph #y=log_5(x-1)+3#?

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Answer 1 · 2017-11-22T11:16:22

See below.

#y = log_5(x-1)+3#

Remember: #log_a x = lnx/lna#

#:. log_5 (x-1) = ln(x-1)/ln5#

Hence, #log_5(x-1)# can be graphed as the function transformed to natural logs above. As shown below.

graph{ln(x-1)/ln5 [-14.24, 14.23, -7.12, 7.12]}

The constant term #+3# simply shifts the graph 3 units positive ("up") the #y-#axis.

The resultant graph of #y# is shown below.

graph{ln(x-1)/ln5 +3 [-14.24, 14.23, -7.12, 7.12]}