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Solve the exponential equation $1+e^{3x}=t$

Step-by-step Solution

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Solution

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Final answer to the problem

$x=\frac{\ln\left(t-1\right)}{3}$
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Step-by-step Solution

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Learn how to solve exponential equations problems step by step online. Solve the exponential equation 1+e^(3x)=t. We need to isolate the dependent variable x, we can do that by simultaneously subtracting 1 from both sides of the equation. 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=3x. Divide both sides of the equation by 3.

Final answer to the problem

$x=\frac{\ln\left(t-1\right)}{3}$

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Function Plot

Plotting: $1+e^{3x}-t$

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1
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5
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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
D□x
∫
∫◻
|◻|
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:

Similar Problems Solved

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$2^{6x+7}=\left(\frac{1}{8}\right)^{1-5x}$

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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