Solve the exponential equation $4^x=32$

Step-by-step Solution

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Final answer to the problem

$x=\frac{5}{2}$
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Apply the formula: $x^b$$=pfgmin\left(x\right)^b$, where $b=x$ and $x=4$

$\left(2^{2}\right)^x=32$

Learn how to solve equazioni esponenziali problems step by step online.

$\left(2^{2}\right)^x=32$

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Learn how to solve equazioni esponenziali problems step by step online. Solve the exponential equation 4^x=32. Apply the formula: x^b=pfgmin\left(x\right)^b, where b=x and x=4. Simplify \left(2^{2}\right)^x using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals x. Apply the formula: x^a=y\to x^a=pfgg\left(y,x\right), where x^a=y=2^{2x}=32, a=2x, x=2, y=32 and x^a=2^{2x}. Apply the formula: a^b=a^c\to b=c, where a=2, b=2x and c=5.

Final answer to the problem

$x=\frac{5}{2}$

Exact Numeric Answer

$x=2.5$

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Function Plot

Plotting: $4^x-32$

SnapXam A2
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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
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

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