2 years ago

Please help I have one question.

Mathematics

1 answer:

Pachacha [2.7K]2 years ago

7 0

1/3 and 5 is the answer.

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I NEED HELP!! please show all work

PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

$4^{5x} = 3^{x-2}$

$\implies \log 4^{5x} = \log 3^{x-2}$

Drop the exponents:

$\implies 5x \log 4 = (x-2) \log 3$

Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing x to the left side and factor out x :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

$\implies x (5 \log 4 - \log 3) = - 2 \log 3$

Solve for x by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

$\implies \boxed{x = -\log_{\frac{1024}3}9}$

5 0

2 years ago

What is the scale factor of 8in=200mi?

BigorU [14]

200 / 8 = 25

scale factor is 1:25 or 0.04

8 0

3 years ago

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In the figure below the measure of <1=5x°, the measure of <2=y°, and the measure of <3=85°. Find the value of each vari

elena-14-01-66 [18.8K]

Answer:

y=95

Step-by-step explanation:

17x5=85

180-85=95

y=95

7 0

2 years ago

A triangle has angles that measure 46 and 84 what is the third angle?

pentagon [3]

The measure of the third angle is 50 because a triangle has a sum of 180 degrees by angle.

so... 46+84=130 and to get to 180, the last angle has to be worth 50.

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3 years ago

A tomato plant grew an average of 0.06 m per day. How many days did it take for the plant to grow a total of 0.96 m.

Nadya [2.5K]

If you divide 96 by 6 then you get 16. So it's 16 days!

3 0

3 years ago

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