Solve the exponential equation $125^{\left(6-5x\right)}=5^{\left(x^2+72\right)}$

Step-by-step Solution

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Final answer to the problem

$x=-6,\:x=-9$
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Step-by-step Solution

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Decompose $125$ in it's prime factors

$\left(5^{3}\right)^{\left(6-5x\right)}=5^{\left(x^2+72\right)}$

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$\left(5^{3}\right)^{\left(6-5x\right)}=5^{\left(x^2+72\right)}$

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Learn how to solve exponential equations problems step by step online. Solve the exponential equation 125^(6-5x)=5^(x^2+72). Decompose 125 in it's prime factors. Simplify \left(5^{3}\right)^{\left(6-5x\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals 6-5x. If the bases are the same, then the exponents must be equal to each other. Solve the product 3\left(6-5x\right).

Final answer to the problem

$x=-6,\:x=-9$

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Function Plot

Plotting: $125^{\left(6-5x\right)}- 5^{\left(x^2+72\right)}$

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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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