# What transformation has changed the parent function f(x) = log5x to its new appearance shown in the graph below logarithmic graph passing through point 5, negative 2.

QUESTION POSTED AT 02/06/2020 - 01:34 AM

QUESTION POSTED AT 02/06/2020 - 01:34 AM

f(x)=log(5x)

We want the curve to pass through (5,-2)

We can move the curve along the plot adding something in the formula. Let’s call that z.

You can put z in different parts of the formula and still find a z value that makes it pass through the point (5,-2). I will choose to put it inside the log:

f(x)=log(5x+z)

f(5)=-2

log(5*5+z)=-2

log(25+z)=-2

10^-2 = 25+z

10^-2 – 25 = z

z=1/100-25 = 1/100-2500/100=-2499/100 = -24.99

Let’s verify:

f(5)= log(5*5-24.99)=-2

So the formula: f(x)=log(5x-24.99) passes through the point (5,-2)

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