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Solve the exponential equation $26^{\left(9x+5\right)}=1$

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 Final answer to the problem

$x=-\frac{5}{9}$
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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
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1

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

$\log_{26}\left(26^{\left(9x+5\right)}\right)=\log_{26}\left(1\right)$

Learn how to solve problems step by step online.

$\log_{26}\left(26^{\left(9x+5\right)}\right)=\log_{26}\left(1\right)$

Learn how to solve problems step by step online. Solve the exponential equation 26^(9x+5)=1. We can take out the unknown from the exponent by applying logarithms in base 10 to both sides of the equation. Evaluating the logarithm of base 26 of 1. 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 5 from both sides of the equation.

 Final answer to the problem

$x=-\frac{5}{9}$

$x=-\frac{5}{9}$

 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

Go!
1
2
3
4
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