Question

the parent function f(x)=log^5x has been transformed by reflecting it over the x-axis stretching it vertically by a factor of two and shifting it up three units. which function is representative of this transformation/ g(x)=-2log^5(x)+3, g(x)=log^5...(2x)-3, g(x)=log^5(-2x)+3, g(x)=2log^5(x)-3

Answer 1

g(x)=-2log_3(x)-5

Step-by-step explanation:

i got it right

Answer 2

log7(x) = log4(x)

Change of base formula:

logA x = logB x / logB a

Changing to base E:

log7(x) = logE(x)/logE(7) = ln(x)/ ln(7)

log4(x) = lonE(x)/logE(4) = ln(x)/ln(4)

So they are equal when :

ln(x)/ln(7) = ln(x)/ln(4)

cross multplying:

ln(x)*ln(4) = ln(x)*ln(7)

ln(x)*ln(4) - ln(x)*ln(7) = 0 <--- everybody to left side

ln(x) * [ ln(4) - ln(7)] = 0 <--- factors out ln(x)

Let k = [ ln(4) - ln(7) ] is a fixed number constant.

Then,

ln(x) * k = 0

dividing both sides by k, cancels it out.

ln(x) = 0 whieans x=1.

So they are equal when x=1

Check:

For x=

log7(1) = log4(1)

is the same as asking the question:

7^x = 1 = 4^x are both equal to 1 where x is the

same exponent in both....

Of course, any number to power zer0 is 1. So x=1.

The graph in