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# Solve the exponential equation $4^x=16\sqrt{128}$

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##  Final answer to the problem

$x=\frac{\log_{2}\left(181.019336\right)}{2}$
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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.
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Calculate the power $\sqrt{128}$

$4^x=16\cdot 8\sqrt{2}$

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

$4^x=16\cdot 8\sqrt{2}$

Learn how to solve exponential equations problems step by step online. Solve the exponential equation 4^x=16128^1/2. Calculate the power \sqrt{128}. Multiply 16 times 11.3137. Decompose 4 in it's prime factors. 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.

##  Final answer to the problem

$x=\frac{\log_{2}\left(181.019336\right)}{2}$

$x=\frac{15}{4}$

##  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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0
a
b
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g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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.