Write the following cubes in expanded form .

Log16^*+log4^*+log2^*=7

ale4655 [162]

Answer:

$x = 16$

Step-by-step explanation:

Given

$log_{16}(x) + log_4(x) + log_2(x) = 7$

Required

Solve for x

$log_{16}(x) + log_4(x) + log_2(x) = 7$

Change base of 16 and base of 4 to base 2

$\frac{log_2(x)}{log_2(16)} + \frac{log_2(x)}{log_2(4)} + log_2(x) = 7$

Express 16 and 4 as 2^4 and 2^2 respectively

$\frac{log_2(x)}{log_2(2^4)} + \frac{log_2(x)}{log_2(2^2)} + log_2(x) = 7$

The above can be rewritten as:

$\frac{log_2(x)}{4log_22} + \frac{log_2(x)}{2log_22} + log_2(x) = 7$

$log_22 = 1$

So, we have:

$\frac{log_2(x)}{4*1} + \frac{log_2(x)}{2*1} + log_2(x) = 7$

$\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x) = 7$

Multiply through by 4

$4(\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x)) = 7 * 4$

$log_2(x) + 2}log_2(x) + 4log_2(x) = 28$

$7log_2(x) = 28$

Divide through by 7

$\frac{7log_2(x)}{7} = \frac{28}{7}$

$log_2(x) = 4$

Apply the following law of logarithm:

If $log_ab = c$ Then $b = a^c$

So, we have:

$x = 2^4$

$x = 16$

6 0

3 years ago

Solve equation Y=9x-70 and y=2x-32

N76 [4]

Step-by-step explanation:

y = 9x - 70 ...1

y = 2x - 32 ...2

...1 - ...2

0 = 7x -38 ...3

7x - 38 = 0

7x = 38

x = 38/7

5 0

3 years ago

PLEASE HELP I GIVE THANKS

jonny [76]

Corresponding angles are angles that are equal in degrees and in this case it is <8 and <4 but there is also <5 and<7.

7 0

3 years ago

If you plot the point -8.85 on a number line, would you place it to the left or right of -8.8?

Ilya [14]

You would place it on the left.

-8.85 < -8.8

7 0

3 years ago

A jet climbs at a steady rate at an angle of inclination of 0.5 degree during game off what will its he height be after a 2.2 km

Aneli [31]

A right triangle will be formed with 2.2 km as the hypotenuse, 0.5 degrees as the angle, and an unknown height (see attachment).

Recall the trigonmetric ratios sine, cosine, and tangent that can be used for right triangles.
Sinθ = opposite side/hypotenuse
Cosθ = adjacent side/hypotenuse
tanθ = opposite side / adjacent side
θ (theta) refers to the angle (not the right angle). In this case, θ is the given angle of 0.5°.

In this problem, you will use sine because there is a side opposite to the angle (the unknown side h) and the hypotenuse, and sine relates those two sides.

Let the variable h represent the unknown opposite side, the height.
sin(0.5°) = h / (2.2km)
h = (2.2km)sin(0.5°)
h = 0.019 km

Hope I helped! If you have questions on any of the steps, please comment below.

3 0

3 years ago