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Solve the exponential equation $3^{\left(x+1\right)}=4^{\left(x-1\right)}$

Step-by-step Solution

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Solution

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Final answer to the problem

$x=\frac{-\ln\left(12\right)}{\ln\left(\frac{3}{4}\right)}$
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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 3^(x+1)=4^(x-1). Apply natural logarithm to both sides of the equation. Solve the product \ln\left(3\right)\left(x+1\right). Solve the product \ln\left(4\right)\left(x-1\right). Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side.

Final answer to the problem

$x=\frac{-\ln\left(12\right)}{\ln\left(\frac{3}{4}\right)}$

Exact Numeric Answer

$x=8.6376834$

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Function Plot

Plotting: $3^{\left(x+1\right)}- 4^{\left(x-1\right)}$

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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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$56^{3x-8}=1$

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$2^{x-1}=3^{2x-1}$

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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