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Solve the exponential equation $56^{\left(3x-8\right)}=1$

Step-by-step Solution

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Solution

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Final answer to the problem

$x=\frac{8}{3}$
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Step-by-step Solution

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Learn how to solve exponential equations problems step by step online. Solve the exponential equation 56^(3x-8)=1. Decompose 56 in it's prime factors. 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. Calculate the power 2^{3}.

Final answer to the problem

$x=\frac{8}{3}$

Exact Numeric Answer

$x=2.6666667$

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Function Plot

Plotting: $56^{\left(3x-8\right)}-1$

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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
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

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

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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