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

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Solution

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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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We can take out the unknown from the exponent by applying logarithms in base $10$ to both sides of the equation

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

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

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Learn how to solve exponential equations problems step by step online. Solve the exponential equation 2^(6x+7)=(1/8)^(1-5x). We can take out the unknown from the exponent by applying logarithms in base 10 to both sides of the equation. Use the following rule for logarithms: \log_b(b^k)=k. We need to isolate the dependent variable x, we can do that by simultaneously subtracting 7 from both sides of the equation. Canceling terms on both sides.

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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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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:

Similar Problems Solved

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

$7^{2x+1}=3^{x+2}$

$3^{x+1}=4^{x-1}$

$4^{x-10}=\left(\frac{1}{64}\right)^{5x+2}$

$56^{3x-8}=1$

$4^{9-6x}=\left(\frac{1}{64}\right)^{\frac{10}{3}}$

$2^{x-1}=3^{2x-1}$

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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