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Check my precalc

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what is the f inverse of f(x)= ln(x-3)
I got y= e^x - 4

Solve
8 times 10^(2x-7)=3

I do not know how to do this. Do i get 8 and 10 with the same base? How?

Thanks!

  • Check my precalc -

    f(x) = ln(x-3) or
    y = ln(x-3)

    first step of find the inverse is to interchange the x and y variables, so the inverse is

    x = ln(y-3)
    e^x = y-3
    y = e^x + 3

    2.

    8 (10^(2x-7) ) = 3
    10^(2x-7) = .375
    take log of both sides

    log( 10^(2x-7) ) = log .375
    (2x-7) log 10 = log .375, remember log 10 = 1
    2x - 7 = log .375
    x = (7 + log.375)/2 = appr 3.287

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