How do you graph $y = {log}_{5} (x - 1) + 3$ $y=log_5(x-1)+3$ ?

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Answer 1 · 2017-11-22T11:16:22

See below.

$y = {log}_{5} (x - 1) + 3$ $y = log_5(x-1)+3$

Remember: ${log}_{a} x = \frac{ln x}{ln a}$ $log_a x = lnx/lna$

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

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]}

How do you graph y=log_5(x-1)+3y=log5(x−1)+3y=log_5(x-1)+3?