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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Apply the formula: $a^x=b$$\to \log_{a}\left(a^x\right)=\log_{a}\left(b\right)$, where $a=26$, $b=1$ and $x=9x+5$

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

Learn how to solve equazioni esponenziali problems step by step online.

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

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Learn how to solve equazioni esponenziali problems step by step online. Solve the exponential equation 26^(9x+5)=1. Apply the formula: a^x=b\to \log_{a}\left(a^x\right)=\log_{a}\left(b\right), where a=26, b=1 and x=9x+5. Apply the formula: \log_{a}\left(b\right)=logf\left(b,a\right), where a=26, b=1 and a,b=26,1. Apply the formula: \log_{b}\left(b^a\right)=a, where a=9x+5 and b=26. Apply the formula: x+a=b\to x+a-a=b-a, where a=5, b=0, x+a=b=9x+5=0, x=9x and x+a=9x+5.

Final answer to the problem

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

Exact Numeric Answer

$x=-0.5555556$

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Function Plot

Plotting: $26^{\left(9x+5\right)}-1$

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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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