Precalculus

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This is for solving exponential/logarithmic functions:

(This is a base e Logarithmic function I would assume):

e^(4x)/10 =4^x-2 ?

I understand the properties of logs for the most part, but I have a hard time figuring out the step-by-step process on how to solve exponential/log equations? Is your first step always to take the ln of both sides, or is that only for certain types of equations? I need a a step to step list on how to work this, to where I can understand and it's just not all math book definitions. For example, I tried to write out my own process such as:

log equations:
1. take log of both sides
2. drop logs
3. multiply
4. distribute
5. standard form
6. solve

Would this be correct?

  • Precalculus -

    for exponentials,

    1. collect exponent stuff on one side
    2. take logs
    add/subtract terms to get x's on one side
    divide by coefficient to get x alone

    for the above one,

    e^(4x)/10 =4^x-2
    e^(4x) = 10*4^x - 20

    not much you can do now. That pesky -20 gets in the way.

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