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# Taking e to both sides [Solved!]

### My question

Your Integration Chapter: The Basic Logarithmic Form, example 4.

Can you show how you took e to both sides to arrive at your result please?

### Relevant page

2. Integration: The Basic Logarithm Form

### What I've done so far

After integrating, t = ln 20 - ln (20-v).

You applied log laws to get t = ln(20/(20-v)).

You took "e to both sides" to get e^t = 20/20-v.

We thought by taking e to both sides the result would be the exponents equated:

t = 20/20-v.

X

Your Integration Chapter: The Basic Logarithmic Form, example 4.

Can you show how you took e to both sides to arrive at your result please?
Relevant page

<a href="https://www.intmath.com/methods-integration/2-integration-logarithmic-form.php">2. Integration: The Basic Logarithm Form</a>

What I've done so far

After integrating, t = ln 20 - ln (20-v).

You applied log laws to get t = ln(20/(20-v)).

You took "e to both sides" to get e^t = 20/20-v.

We thought by taking e to both sides the result would be the exponents equated:

t = 20/20-v.

## Re: Taking e to both sides

@Phinah: The opposite process of taking the "log" of something is to take "e to the power of...".

Writing the full details would be:

t = ln (20 /(20-v))

e^t = e^[ln (20/(20-v))]

e^t = 20/(20-v)

e^t = e^[(20/(20-v))] (without "ln")

t = 20/(20-v)

but that's not what we started with.

A similar situation is the case where "raising to power 2" is the opposite of "square root".

y = sqrt(x+2)

Squaring both sides gives us:

y^2 = (sqrt(x+2))^2 = x+2

The "power 2" has "undone" the sqrt operation.

Similarly, the "e to the power" operation undoes the "ln" expression in the example you are asking about.

Hope it makes sense.

X

@Phinah: The opposite process of taking the "log" of something is to take "e to the power of...".

Writing the full details would be:

t = ln (20 /(20-v))

e^t = e^[ln (20/(20-v))]

e^t = 20/(20-v)

e^t = e^[(20/(20-v))] (without "ln")

t = 20/(20-v)

but that's not what we started with.

A similar situation is the case where "raising to power 2" is the opposite of "square root".

y = sqrt(x+2)

Squaring both sides gives us:

y^2 = (sqrt(x+2))^2 = x+2

The "power 2" has "undone" the sqrt operation.

Similarly, the "e to the power" operation undoes the "ln" expression in the example you are asking about.

Hope it makes sense.

## Re: Taking e to both sides

It does now. Thank you.

X

It does now.  Thank you.