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# Solve the exponential equation $3^{2x}=14$

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##  Final answer to the problem

$x=\frac{\log_{3}\left(14\right)}{2}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Find the derivative using the definition
• Solve by quadratic formula (general formula)
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
Can't find a method? Tell us so we can add it.
1

We can take out the unknown from the exponent by applying logarithms in base $10$ to both sides of the equation

$\log_{3}\left(3^{2x}\right)=\log_{3}\left(14\right)$

Learn how to solve special products problems step by step online.

$\log_{3}\left(3^{2x}\right)=\log_{3}\left(14\right)$

Learn how to solve special products problems step by step online. Solve the exponential equation 3^(2x)=14. We can take out the unknown from the exponent by applying logarithms in base 10 to both sides of the equation. Use the following rule for logarithms: \log_b(b^k)=k. Divide both sides of the equation by 2.

##  Final answer to the problem

$x=\frac{\log_{3}\left(14\right)}{2}$

$x=1.2010868$

##  Explore different ways to solve this problem

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

SnapXam A2

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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

###  Main Topic: Special Products

Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.