Solve 6^(4x+1)=5^(x-3) for x

Mathematics

2 answers:

AleksandrR [38]4 years ago

8 0

$6^{4x+1}=5^{x-3}\\\\\log6^{4x+1}=\log5^{x-3}\\\\(4x+1)\log 6=(x-3)\log 5\\\\(4x+1)\log 6-(x-3)\log 5=0\\\\4x\log 6+\log 6-x\log 5+3\log 5=0\\\\4x\log 6-x\log 5 = -3\log 5-\log 6\\\\x(4\log 6-\log 5) = -3\log 5-\log 6\\\\x=\dfrac{-3\log 5-\log 6}{4\log 6-\log 5}\\\\x=\dfrac{3\log 5+\log 6}{\log 5-4\log 6}$

myrzilka [38]4 years ago

7 0

Answer: The answer is C

Step-by-step explanation:

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The diagram represents the shape and dimensions of Kayla's garden. A special fertilizer is used for the vegetable garden. Each b

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Answer:

B. 18 bags

Step-by-step explanation:

First you need to determine the area of the vegetable garden. The vegetable garden is a rectangle with the following dimensions:

L = 24 ft

W = 9 ft

The Formula for the area of a rectangle is:

$A = L\times W$

So let's solve it:

$A = L\timesW\\A = 24 ft\times9ft\\A= 216ft^{2}$

With that, we can figure out how many bags of fertilizer would be needed by dividing the area of the vegetable garden by how much one bag of fertilizer covers:

$\dfrac{214ft^2}{12ft^2/bag}=18\;bags$