Find a number such that 10 less than two thirds the number is one fourth the number

Mathematics

1 answer:

Ivan3 years ago

3 0

Answer:

the number is 24

Step-by-step explanation:

10 less than two thirds the number is one fourth the number

Let the unknown number be x

two third of the number is $\frac{2}{3} x$

10 less than two third the number becomes

$\frac{2}{3}x-10$

one fourth the number becomes $\frac{1}{4}x$

10 less than two thirds the number is one fourth the number

$\frac{2}{3}x-10=\frac{1}{4}x$

We need to solve for x

LCD is 3*4 = 12

Multiply the whole equation by 12

$\frac{2*12}{3}x-10*12=\frac{1*12}{4}x$

8x - 120 = 3x

add 120 on both sides

8x = 3x + 120

Subtract 3x on both sides

5x = 120

divide by 5 on both sides

x= 24

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Can someone please write this as a single logarithm and show work please and thank you

Mazyrski [523]

Answer:

$log_b(w^3y^4)$

Step-by-step explanation:

To write the expression as a single logarithm, or condense it, use the properties of logarithms.

1) The power property of logarithms states that $log_ax^r = rlog_ax$ . In other words, the exponent within a logarithm can be brought out in front so it's multiplied by the logarithm. This means that the number in front of the logarithm can also be brought inside the logarithm as an exponent.

So, in this case, we can move the 3 and the 4 inside the logarithms as exponents. Apply this property as seen below:

$3log_bw+4log_by\\=log_bw^3+log_by^4$

2) The product property of logarithms states that $log_axy = log_ax+log_ay$ . In other words, the logarithm of a product is equal to the sum of the logarithms of its factors. So, in this case, write the expression as a single logarithm by taking the log (keep the same base) of the product of $w^3$ and $y^4$ . Apply the property as seen below and find the final answer.