## Fractional exponents with a variable: (844)3^(t/4)=22788

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
baronthered
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### Fractional exponents with a variable: (844)3^(t/4)=22788

I'm having trouble remembering how to solve for the variable in the fractional exponent. An example would be (844)3t/4=22788. I know both sides divided by 844 gives 27=3t/4 or 33=3t/4 I'm trying to solve for t (Growth over time problem). Thanks in advance.

stapel_eliz
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...(844)3t/4=22788. I know both sides divided by 844 gives 27=3t/4 or 33=3t/4 I'm trying to solve for t (Growth over time problem).
You've already done the hard part!

For this sort of exponential equation, once you've got an equation with the same base on either side of the "equals" sign, just equate the powers, and solve the resulting equation. For instance:

. . . . .$8^{3x+2}\, =\, 16^{5-x}$

. . . . .$(2^3)^{3x+2}\, =\, (2^4)^{5-x}$

. . . . .$2^{3(3x+2)}\, =\, 2^{4(5-x)}$

. . . . .$3(3x\, +\, 2)\, =\, 4(5\, -\, x)$

...and so forth.

baronthered
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Joined: Mon Apr 06, 2009 10:55 pm
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### Re: Fractional exponents with a variable: (844)3^(t/4)=22788

the t/4 should read as t divided by 4. I'm trying to isolate t I'm thinking I need to multiply both sides of the exponents by 4 to even things up. I never can remember the exact rules for this.

stapel_eliz
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Is my previous reply not displaying for you? (I'd explained the process, provided a link to a lesson with an explanations and many worked examples, and provided a similar example, but you don't seem aware of the contents...?)