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Solve the exponential equation $2^x8^{\left(5x-1\right)}=64^x$

Step-by-step Solution

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Final answer to the problem

$x=\frac{3}{10}$
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Step-by-step Solution

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Decompose $8$ in it's prime factors

$2^x\left(2^{3}\right)^{\left(5x-1\right)}=64^x$

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$2^x\left(2^{3}\right)^{\left(5x-1\right)}=64^x$

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Learn how to solve problems step by step online. Solve the exponential equation 2^x8^(5x-1)=64^x. Decompose 8 in it's prime factors. Simplify \left(2^{3}\right)^{\left(5x-1\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 5x-1. Apply the exponent property of product of powers: x^a\cdot x^b=x^{a+b}. Rewrite the power 64^x with base 2.

Final answer to the problem

$x=\frac{3}{10}$

Exact Numeric Answer

$x=\frac{3}{10}$

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Function Plot

Plotting: $2^x8^{\left(5x-1\right)}- 64^x$

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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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