Calculus > Eliminate Exponents in Calculus

Exponents can be a tricky factor in dealing with equations, and when exponents have variables in them it becomes even more complicated. It’s possible to **eliminate some exponents** using the The Power Rule, but this won’t work for exponents over 2. Another way to eliminate exponents in calculus is to convert exponential variables into a more manageable form, known as the **logarithm function.**

A logarithm represents the value y the base, b, has to be raised to to equal the value x in the form of log_b(x). If x=b

^{y,}then log_b(x)=y. Not every log is listed with a base b, and these are considered to use the common base of 10. The log might also appear in the form ln(x), which is a log taken to the base of e, the natural number.

## How to Eliminate Exponents in Calculus: Example

Sample Problem: Solve for the value of x if 10 to the 5x power plus 10 is equal to 20.

Step 1: **Set up the equation **from the information given in the question.

10^{5x} + 10 = 20

Step 2: **Take 10 from both sides **to eliminate the 10 near the variable. This is a basic algebra step, but still an important one.

10^{5x} + 10 – 10 = 20 – 10

giving:

10^{5x} = 10

Step 3: **Take the log** of both sides.

log(10^{5x}) = log(10)

Step 4: Apply the rule that states log_b(a^{c}) = c * log_b(a). Using this, we can move the variable out of the exponent and leave it in a form we can simplify. If you recall that a log without a subscript is considered a base of 10, you can easily simplify log_10(10) = y as 1, due to b^{y} = x being 10^{1} = 10.

5x * 1 = 1

Step 5: Divide both sides by 5 to** isolate the variable.** This will give you a final answer of 1/5, or .2.

5x/5 = 1/5 -> x = 1/5 = 0.2

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How to Eliminate Exponents in Calculus was last modified: October 12th, 2017 by **

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2^5x +10 -10 = 20-10

would seem to give

2^5x = 10

rather than

10^5x=10

You’re right. The 2 was a typo. Now fixed, thank you!