Solve the exponential equation $2^{\left(6x+7\right)}=\left(\frac{1}{8}\right)^{\left(1-5x\right)}$

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Final answer to the problem

$x=\frac{\log_{2}\left(\frac{1}{8}\right)-7}{6+5\log_{2}\left(\frac{1}{8}\right)}$
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Step-by-step Solution

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Apply the formula: $a^x=b$$\to \log_{a}\left(a^x\right)=\log_{a}\left(b\right)$, where $a=2$, $b=\left(\frac{1}{8}\right)^{\left(1-5x\right)}$ and $x=6x+7$

$\log_{2}\left(2^{\left(6x+7\right)}\right)=\log_{2}\left(\left(\frac{1}{8}\right)^{\left(1-5x\right)}\right)$

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$\log_{2}\left(2^{\left(6x+7\right)}\right)=\log_{2}\left(\left(\frac{1}{8}\right)^{\left(1-5x\right)}\right)$

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Learn how to solve equazioni esponenziali problems step by step online. Solve the exponential equation 2^(6x+7)=(1/8)^(1-5x). Apply the formula: a^x=b\to \log_{a}\left(a^x\right)=\log_{a}\left(b\right), where a=2, b=\left(\frac{1}{8}\right)^{\left(1-5x\right)} and x=6x+7. Apply the formula: \log_{b}\left(b^a\right)=a, where a=6x+7 and b=2. Apply the formula: x+a=b\to x+a-a=b-a, where a=7, b=\log_{2}\left(\left(\frac{1}{8}\right)^{\left(1-5x\right)}\right), x+a=b=6x+7=\log_{2}\left(\left(\frac{1}{8}\right)^{\left(1-5x\right)}\right), x=6x and x+a=6x+7. Apply the formula: x+a+c=b+f\to x=b-a, where a=7, b=\log_{2}\left(\left(\frac{1}{8}\right)^{\left(1-5x\right)}\right), c=-7, f=-7 and x=6x.

Final answer to the problem

$x=\frac{\log_{2}\left(\frac{1}{8}\right)-7}{6+5\log_{2}\left(\frac{1}{8}\right)}$

Exact Numeric Answer

$x=1.1111111$

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Function Plot

Plotting: $2^{\left(6x+7\right)}-\left(\frac{1}{8}\right)^{\left(1-5x\right)}$

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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

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