advanced Functions/ Precalculus Log

1. If (x, y) is on the graph f(x) = log(base10)x, state the coordinates (in terms of x and y) that would be on the graph of f(x) = 2log(base10)(x - 4) + 3?

2. Estimate the value of log(base 3)91

Can you please explain how you arrive at the answer since I do't understand them. Thanks! :)

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  1. If we call the 2nd function g(x), then
    g(x) = 2f(x-4)+3

    Not sure what you're after. g is f scaled by a factor of 2 and shifted right by 4 and up 3 units.

    As for log_3(91), I'd just say that since log81 = 4, and 91/81 is about 9/8, which is near 1, I'd just say 4.

    There are many ways to approximate things. A little better explanation of the tools at your disposal would help.

    Note also that log_3(91) = log_10(91)/log_10(3), so that's close to 2/(1/2) = 4.

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