how to discuss exponential equationhow to discuss exponential equation a^f(x)=b? example included

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

`a^f(x)=b`

You should use the logarithms as you use the squaring when you need to remove a square root such that:

Notice that the logarithms have the property to bring down the exponent, as it was proved above.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The way of solving the exponential equation depends on the right term b.

If b is a multiple of a, then the equation could be solved using the one to one property of exponential function.

Let's see how:

2^2x = 8

But 8 is a multiple of 2:

8 = 2^3

2^2x = 2^3

Since the bases are matching, we'll apply one to one property:

2x = 3

x = 3/2

If b is not a multiple of a, then the equation could be solved using logarithms.

2^3x = 3

Since we cannot create matching bases, we'll take logarithms both sides:

lg 2^3x = lg 3

We'll apply product property of logarithms:

3x*lg2 = lg3

3x = lg3/lg2

x = lg3/3lg2

x = lg3/lg8

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