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3 years ago

What does 4^2x-4=1 equal

Mathematics

2 answers:

slega [8]3 years ago

5 0

If the starting equation is

4²ˣ - 4 = 1

first move the 4 on the left to the right side:

4²ˣ = 5

Take the base-4 logarithm of both sides:

log₄(4²ˣ ) = log₄(5)

Drop the exponent on the left, using the property $\log_b(a^n)=n\log_b(a)$ :

2x log₄(4) = log₄(5)

Now $\log_b(b)=1$ for any b, so

2x = log₄(5)

Solve for x by dividing both sides by 2:

x = 1/2 log₄(5)

You can also express this as

x = log₄(√5)

to make the solution slightly more compact.

You can also use the change-of-base identity to rewrite the solution as

x = log(5) / (2 log(4))

where the base of the logarithm is arbitrarily chosen. Then

x = log(5) / log(4²)

x = log(5) / log(16)

x = log₁₆(5)

Lisa [10]3 years ago

4 0

Answer:

x=2

Step-by-step explanation:

4^2x-4=4^0

2x-4=0

2x=4

x=4/2

x=2

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An architect designs a porch support that forms a 42.58 angle with the roof. What is the measure of the angle’s complement? What

antoniya [11.8K]

Measure of the angle’s complement is 47.42 degree and measure of the angle’s supplement is 137.42 degree

Solution:

Given that architect designs a porch support that forms a 42.58 angle with the roof.

To find: measure of the angle’s complement and measure of its supplement

Finding measure of the angle’s complement:

Two angles are Complementary when they add up to 90 degrees

To determine the complement, subtract the given angle from 90

measure of the angle’s complement = 90 - 42.58 = 47.42

Finding measure of the angle’s supplement:

Two angles are supplementary when they add up to 180 degrees

To determine the supplement, subtract the given angle from 180

measure of the angle’s supplement = 180 - 42.58 = 137.42

3 0

3 years ago

-19=6k+9-4K solve for k

oksano4ka [1.4K]

Answer:

-14

Step-by-step explanation:

-19=6k-4k+9

-19=2k+9

subtract 9 from both sides

-28=2k

-14=k

To check your answer plug 14 in for k

8 0

3 years ago

What is the area of the following circle d=14

katen-ka-za [31]

Answer:

A ≈ 153.94

Step-by-step explanation:

3 0

3 years ago

If a substance decays at a rate of 25% every 10 years, how long will it take 512 grams of the substance to decay to 121.5 grams

Juliette [100K]

Answer:

It will take 50 years to decay from 512 grams to 121.5 grams.

Step-by-step explanation:

The decay formula :

$N=N_0e^{-\lambda t}$

where

N= amount of substance after t time

N₀= initial of substance

t= time.

A substance decays at a rate 25% every 10 years.

So, remaining amount of the substance is = (100%-25%)= 75%

$\frac{N}{N_0}=\frac{75\%}{100\%}=\frac{75}{100}=\frac34$ , t= 10

$N=N_0e^{-\lambda t}$

$\Rightarrow \frac {N}{N_0}=e^{-\lambda t}$

$\Rightarrow \frac34 =e^{-\lambda .10}$

Taking ln both sides

$\Rightarrow ln|\frac34| =ln|e^{-\lambda .10}|$

$\Rightarrow ln|\frac34|=-10\lambda$

$\Rightarrow \lambda=\frac{ ln|\frac34|}{-10}$

Now , N₀= 512 grams, N= 121.5 grams, t=?

$N=N_0e^{-\lambda t}$

$\therefore 121.5=512e^{-\frac{ln|\frac34|}{-10}.t}$

$\Rightarrow 121.5=512e^{\frac{ln|\frac34|}{10}.t}$

$\Rightarrow \frac{121.5}{512}=e^{\frac{ln|\frac34|}{10}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{121.5}{512}|=ln|e^{\frac{ln|\frac34|}{10}.t}|$

$\Rightarrow ln|\frac{121.5}{512}|={\frac{ln|\frac34|}{10}.t}$

$\Rightarrow t=\frac{ln|\frac{121.5}{512}|}{\frac{ln|\frac34|}{10}}$

$\Rightarrow t=\frac{10.ln|\frac{121.5}{512}|}{{ln|\frac34|}}$

⇒t=50 years

It will take 50 years to decay from 512 grams to 121.5 grams.

8 0

4 years ago

Simplify into one fraction 6/x+7-3/x-2?

makkiz [27]

6/x-3/x= 3/x 7-2=5 (5x+3)/x

4 0

4 years ago