Pre-Calculus



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Do you know the following?

a^(n + m) = a^n * a^m

Use it! 8-)

How about the following example.

4^(x - 7) = 1/256

I'll use the following property, to separate x from -7 (i.e., the first step toward isolating x).

a^(n - m) = a^n/a^m

4^x/4^7 = 1/256

Multiply both sides by 4^7

4^x = 4^7 * 1/256

Simplify the righthand side, using a calculator.

4^x = 64

Since 4^3 is 64, x = 3.

If you don't know squares and cubes of small Natural numbers, then switch to logarithm form.

x = log_4(64)

Change of base formula gives the following.

x = log(64)/log(4)

Use a calculator to find x = 3

Can you separate the x from the 1, in your exercise? 8-)

In other words, what factored product of two powers of 3 equals 3^(x + 1) ?

 
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