What is written as a 2log5(5x^3)+(1/3)log5((x^2)+6) single logarithm?

2 answers:

8 0

$2 \times log_{5}( {5x}^{3} ) + ( \frac{1}{3} ) \times log_{5}((x {}^{2}) + 6 )$

is equals to
$log_{5}(25 {x}^{6} \times \sqrt[3]{x {}^{2} + 6 } )$

svetlana [45]3 years ago

4 0

Answer: The required expression using single logarithm is $\log_5\{25x^6(x^2+6)^\frac{1}{3}\}.$

Step-by-step explanation: We are given to write the following logarithmic expression as a single logarithm :

$L=2\log_5(5x^3)+\dfrac{1}{3}\log_5(x^2+6).$

We will be using the following properties of logarithms :

$(i)~a\log b=\log b^a,\\\\(ii)~\log a+\log b=\log (ab).$

We have

$L\\\\=2\log_5(5x^3)+\dfrac{1}{3}\log_5(x^2+6)\\\\=\log_5(5x^3)^2+\log_5(x^2+6)^\frac{1}{3}\\\\=\log_5\{(5x^3)^2\times (x^2+6)^\frac{1}{3}\}\\\\=\log_5\{25x^6(x^2+6)^\frac{1}{3}\}.$

Thus, the required expression using single logarithm is $\log_5\{25x^6(x^2+6)^\frac{1}{3}\}.$

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Tom planted 1/2 of an 8-ft by 9-ft garden with vegetables. He planted tomatoes in 1/3 of the vegetable garden and corn in the re

ser-zykov [4K]

Answer:

Corn was planted in 24 sq.ft. of the vegetable garden.

Step-by-step explanation:

Length of garden = 9 ft

width of garden = 8 ft

Hence we will first find the total area of garden.

Total area of garden = length × width = $8 \times 9 = 72ft^2$

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Hence.

Area of Vegetables garden = $\frac{1}{2}\times \textrm{Total Area of Garden} = \frac{1}{2}\times 72 = 36ft^2$

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Area in which tomatoes was planted = $\frac{1}{3}\times \textrm{Area of Vegetables Garden} = \frac{1}{3}\times 36 = 12ft^2$

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Hence Area of vegetable garden in which corn was planted is 24 sq.ft.

7 0

3 years ago

Points A B C D and E are collinear and in that order. Find AC if AE=x+50 and CE=x+32

Lana71 [14]

Answer:

Step-by-step explanation:

Points A B C D and E are collinear.

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