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# Solve the exponential equation $32^{\left(x^2-5x-3\right)}=1$

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##  Final answer to the problem

$x=5.5413813,\:x=-0.5413813$
Got another answer? Verify it here!

##  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

Decompose $32$ in it's prime factors

$\left(2^{5}\right)^{\left(x^2-5x-3\right)}=1$

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

$\left(2^{5}\right)^{\left(x^2-5x-3\right)}=1$

Learn how to solve exponential equations problems step by step online. Solve the exponential equation 32^(x^2-5x+-3)=1. Decompose 32 in it's prime factors. Simplify \left(2^{5}\right)^{\left(x^2-5x-3\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 5 and n equals x^2-5x-3. Solve the product 5\left(x^2-5x-3\right). Multiply the single term 5 by each term of the polynomial \left(-5x-3\right).

##  Final answer to the problem

$x=5.5413813,\:x=-0.5413813$

##  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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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

###  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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