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Solve the exponential equation $e^{\left(3-2x\right)}=4$

Step-by-step Solution

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Final answer to the problem

$x=\frac{\ln\left(4\right)-3}{-2}$
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Step-by-step Solution

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We can take out the unknown from the exponent by applying natural logarithm to both sides of the equation

$\ln\left(e^{\left(3-2x\right)}\right)=\ln\left(4\right)$

Learn how to solve exponential equations problems step by step online.

$\ln\left(e^{\left(3-2x\right)}\right)=\ln\left(4\right)$

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Learn how to solve exponential equations problems step by step online. Solve the exponential equation e^(3-2x)=4. We can take out the unknown from the exponent by applying natural logarithm to both sides of the equation. Apply the formula: \ln\left(e^x\right)=x, where x=3-2x. We need to isolate the dependent variable x, we can do that by simultaneously subtracting 3 from both sides of the equation. Canceling terms on both sides.

Final answer to the problem

$x=\frac{\ln\left(4\right)-3}{-2}$

Exact Numeric Answer

$x=0.8068528$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $e^{\left(3-2x\right)}-4$

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Answer Assistant

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Got a different answer? Verify it!

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Exponential Equations

Exponential equations are those where the unknown appears only in the exponents of powers of constant bases.

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