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

Step-by-step Solution

Go!
Symbolic mode
Text mode
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

Final answer to the problem

$x=\frac{2\log_{4}\left(\frac{1}{64}\right)+10}{1-5\log_{4}\left(\frac{1}{64}\right)}$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Choisir une option
  • Résoudre pour x
  • Simplifier
  • Facteur
  • Trouver les racines
  • Load more...
Can't find a method? Tell us so we can add it.
1

Apply the formula: $a^x=b$$\to \log_{a}\left(a^x\right)=\log_{a}\left(b\right)$, where $a=4$, $b=\left(\frac{1}{64}\right)^{\left(5x+2\right)}$ and $x=x-10$

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

Learn how to solve intégrales trigonométriques problems step by step online.

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

With a free account, access a part of this solution

Unlock the first 3 steps of this solution

Learn how to solve intégrales trigonométriques problems step by step online. Solve the exponential equation 4^(x-10)=(1/64)^(5x+2). Apply the formula: a^x=b\to \log_{a}\left(a^x\right)=\log_{a}\left(b\right), where a=4, b=\left(\frac{1}{64}\right)^{\left(5x+2\right)} and x=x-10. Apply the formula: \log_{b}\left(b^a\right)=a, where a=x-10 and b=4. Apply the formula: x+a=b\to x+a-a=b-a, where a=-10, b=\log_{4}\left(\left(\frac{1}{64}\right)^{\left(5x+2\right)}\right), x+a=b=x-10=\log_{4}\left(\left(\frac{1}{64}\right)^{\left(5x+2\right)}\right) and x+a=x-10. Apply the formula: x+a+c=b+f\to x=b-a, where a=-10, b=\log_{4}\left(\left(\frac{1}{64}\right)^{\left(5x+2\right)}\right), c=10 and f=10.

Final answer to the problem

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

Exact Numeric Answer

$x=0.25$

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

Help us improve with your feedback!

Function Plot

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

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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

How to improve your answer:

Your Personal Math Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.

Create an Account