Solve the equation $\frac{5^2- 7^x}{\cos\left(\frac{\pi }{8}\right)}=\frac{9}{5}$

Step-by-step Solution

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Final answer to the problem

$x=\log_{7}\left(\frac{-9\cos\left(\frac{\pi }{8}\right)+125}{5}\right)$
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Step-by-step Solution

How should I solve this problem?

  • Prime Factor Decomposition
  • 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

Calculate the power $5^2$

$\frac{25- 7^x}{\cos\left(\frac{\pi }{8}\right)}=\frac{9}{5}$

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$\frac{25- 7^x}{\cos\left(\frac{\pi }{8}\right)}=\frac{9}{5}$

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Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Solve the equation (5^2-7^x)/cos(pi/8)=9/5. Calculate the power 5^2. Apply fraction cross-multiplication. Divide both sides of the equation by 5. We need to isolate the dependent variable x, we can do that by simultaneously subtracting 25 from both sides of the equation.

Final answer to the problem

$x=\log_{7}\left(\frac{-9\cos\left(\frac{\pi }{8}\right)+125}{5}\right)$

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Function Plot

Plotting: $\frac{5^2- 7^x}{\cos\left(\frac{\pi }{8}\right)}-\frac{9}{5}$

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2
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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

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