Calculators Topics Solving Methods Step Reviewer Go Premium
ENG • ESP
Topics
  1. calculators
  2. Exponential Equations

Exponential Equations Calculator

Get detailed solutions to your math problems with our Exponential Equations step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

Go!
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
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

Example

Solved Problems

Difficult Problems

1

Solved example of exponential equations

$3^x=81$
2

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

$\log \left(3^x\right)=\log \left(81\right)$
3

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$x\log \left(3\right)=\log \left(81\right)$
4

Divide both sides of the equation by $\log \left(3\right)$

$x=\frac{\log \left(81\right)}{\log \left(3\right)}$
5

Apply the change of base formula for logarithms: $\log_b(a)=\frac{\log_x(a)}{\log_x(b)}$

$x=\log_{3}\left(81\right)$
6

Decompose $81$ in it's prime factors

$x=\log_{3}\left(9^{2}\right)$
7

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$x=2\log_{3}\left(9\right)$
8

Decompose $9$ in it's prime factors

$x=2\log_{3}\left(3^{2}\right)$
9

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$x=4\log_{3}\left(3\right)$
10

Evaluating the logarithm of base $3$ of $3$

$x=4\cdot 1$
11

Multiply $4$ times $1$

$x=4$

Final Answer

$x=4$

Struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!