I really need help with this problem.

Question

Consider the function g(x) = 2\log _(3)(x+72)+4

a) Describe the relationship of the graph of g(x) to the graph of f(x) = log_(3) x

b) Find the difference between g and f at x=9

c) for what value(s) of x is g(x) = 12

Answer 1

starts with log_3(x)

shifts 72 units to the left

shifts 4 units upward

takes the reciprocal

multiplies each y-value by 2

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log_3(9) = 2

f(9) = 2

g(9) 2 / {log_3(81) + 4 } = 2/ (4+4) = 2/8 = 1/4

UNLESS you mean...

g(9) = { 2/log_3(81) } + 4 =

= ( 2/ 4) + 4 = 1/2 + 4 = 4 and 1/2 = 9/2

Please use parenthesis to clarify if the 4 is in the denominator or not...

in the former case the difference is 1/4 - 2 = -7/4

in the latter case the difference is 9/2 - 2 = 9/2-4/2 = 5/2

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in the former case

2 / {log_3(x+72) + 4} = 12/1

2 = 12 {log_3(x+72) + 4}

2 = 12 * log_3(x+72) + 48

-46 = 12 * log_3(x+72)

-23/6 = log_3(x+72)

3^(-23/6) = x + 72

x = 3^(-23/6) - 72 = 1/3^(23/6) - 72

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in the latter case

2/log_3(x+72) + 4 = 12

2/log_3(x+72) = 8

2 = 8 * log_3(x+72)

1/4 = log_3(x+72)

3^(1/4) = x+ 72

root4(3) = x + 72

root4(3) - 72 = x