How do you graph $y = 2 + {log}_{6} (x - 2)$ $y=2+log_6(x-2)$ ?

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How do you graph $y = 2 + {log}_{6} (x - 2)$ $y=2+log_6(x-2)$ ?

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Answer 1 · 2016-11-09T23:25:47

Use the property of logarithms ${log}_{c} (f (x)) = \frac{{log}_{b} (f (x))}{{log}_{b} (c)}$ $log_c(f(x)) = log_b(f(x))/log_b(c)$

Explanation:

You can convert to

$y = 2 + \frac{ln (x - 2)}{ln (6)}$ $y = 2 + ln(x - 2)/ln(6)$ or $y = 2 + \frac{{log}_{10} (x - 2)}{{log}_{10} (6)}$ $y = 2 + log_10(x - 2)/log_10(6)$

And generate your table of values using a calculator or spreadsheet.

Here is a graph using the first equation:

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Using the second equation:
enter image source here

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How do you graph $y = 2 + {log}_{6} (x - 2)$ $y=2+log_6(x-2)$ ?

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How do you graph $y = 2 + {log}_{6} (x - 2)$ $y=2+log_6(x-2)$ ?