# 7. Find a number t such that ln(2t + 1) = −4 exact value?

precalc

### 5 Answers

- llafferLv 72 months ago
ln(2t + 1) = -4

Making each side an exponent over a base of "e" will cancel out the natural log and leave only what's inside. Doing that we get:

2t + 1 = e⁻⁴

Now solving for t:

2t = e⁻⁴ - 1

t = (e⁻⁴ - 1) / 2

or:

t = 1/(2e⁴) - 1/2

That's your exact value. A decimal approximation to that would be:

t = -0.4908422

Substituting this into the original equation we can test this value:

ln(2t + 1) = -4

ln[2(-0.4908422) + 1] = -4

ln(-0.9816844 + 1) = -4

ln(0.0183156) = -4

-4.000002 = -4

Since we rounded to 7SF, we should be correct to 6SF. Checking the first 6 SF of the left side it does equal the right side. So this is correct.

Again the answer is:

t = 1/(2e⁴) - 1/2

- fcas80Lv 72 months ago
t can be solved in terms of e. e is irrational. The resulting expression will be exact in terms of e, but it will not be an integer.

- Wayne DeguManLv 72 months ago
ln(2t + 1) = -4

so, 2t + 1 = e⁻⁴

Hence, 2t = e⁻⁴ - 1

so, t = (e⁻⁴ - 1)/2

:)>

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- rotchmLv 72 months ago
Hint: do e^ each side. What does that give?

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