All categories

4 years ago

What is the exact value of x in the exponential equation 2^5x − 57 = 43?

1 answer:

4 0

Start by getting the term with the exponent on one side
$2^{5x}=100$

take the log of both sides
$log 2^{5x} =log100$

There is a log rule that says we can bring down the exponent
$5xlog2=log100$

Solve for x
$5x= \frac{log100}{log2}$
5x=6.64

answer: x=1.33

You might be interested in

Find x: explain if you can!

Sergio039 [100]

Answer:

x is 97

Step-by-step explanation:

the interior angles have to equal 180 and the exterior angles have to come to 360 degrees

so you already know 23 to find the one by the 106 degree you use the linear pair postulate ( angles on a straight line will equal 180) so 180-106 equals 74. Now you have 2 of the three interior angles. To find the third you take 180 - 74 - 23 which equals 83 then you can use the linear pair postulate again and take 180-83 to get your answer for x which equals 97

4 0

3 years ago

A craft store buys 50 yards of satin ribon for $12.50. The store sells the ribbon by the foot. A customer can purchase 5 feet of

amm1812

Answer:

$8.1

Step-by-step explanation:

Convert 45 yards of ribbon to feet through proper conversion factor.

(45 yards)(3 ft / 1 yard) = 135 feet

Divide this number by 5 to determine the number of 5-ft ribbon that customers can purchased.

n = 135 ft / 5 ft = 27

Then, multiply by $0.80.

R = (27)($0.80) = $21.6

The profit is equal to $21.6 and $13.50,

P = $21.6 - $13.50 = $8.1

Answer: $8.1

8 0

3 years ago

Solve for x. The triangles in each pair are similar

liubo4ka [24]

9x +1= 0
9x/9 +1-1=0
X= 9-1
X= 8

3 0

3 years ago

Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.

trasher [3.6K]

Answer:

$\frac{xe^{7x}}{7} + \frac{e^{7x}}{49}$

Step-by-step explanation:

Given the integral equation

$\int\limits{xe^{7x}} \, dx \\$

According to integration by part;

$\int\limits {u} \, dv = uv + \int\limits {v} \, du$

u = x, dv = e^7x

du/dx = 1

du = dx

$v = \int\limits {e^{7x}} \, dx \\v = e^7x/7$

Substitute the given values into the formula;

$\int\limits {xe^{7x}} \, dx = x(e^{7x}/7) + \int\limits ({e^{7x}/7}) \, dx\\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{7*7} \\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{49}$