Question 12 (1 point)

How would you simplify (log 27/logx) x (log x^2/log3)? I don’t think I did this correctly.

Kaylis [27]

Answer:

6

Step-by-step explanation:

logx 27 * log3 x^2

The first step is to convert to base 10

(log 27/logx) * (log x^2/log3)

27 = 3^3 so we can rewrite this

(log 3^3/logx) * (log x^2/log3)

log a^b = b log a

(3 log 3/logx) * (2log x/log3)

We can cancel the log x in the numerator and denominator and the log 3 in the numerator and denominator

3 * 2

6

7 0

3 years ago

Chelsea took out three loans for a total of $ 78 comma 000 78,000 to start an organic orchard. Her business-equipment loan was

lianna [129]

Answer:

Business-equipment loan, A=$15000

Small-business loan, B=$24000

home-equity loan, C= $39000

Step-by-step explanation:

Let the Business-equipment loan at an interest rate of 11%=A

Let the small-business loan was at an interest rate of 5% =B

Let her home-equity loan was at an interest rate of 4.5%.=C

Since her total Loan=$78000

A+B+C=78000....(I)

Simple Interest = (P X R X T)/100

Since the Time, T=1 year

Interest on A = 0.11A

Interest on B = 0.05B

Interest on C = 0.045C

The total simple interest due on the loans in one year was $4605.

0.11A+0.05B+0.045C=4605....(II)

The annual simple interest on the home-equity loan was $105 more than the interest on the business-equipment loan.

0.045C = 0.11A +105...(III)

We proceed to solve the simultaneous equations.

A+B+C=78000....(I)

0.11A+0.05B+0.045C=4605....(II)

0.045C = 0.11A +105...(III)

From (III), 0.045C = 0.11A +105

Substitute 0.045C = 0.11A +105 into (II).

0.11A+0.05B+0.11A +105=4605

0.22A+0.05B=4500

From (III),

$C=\frac{22A}{9}+\frac{7000}{3}$

Substitute into (I)

$A+B+\frac{22A}{9}+\frac{7000}{3}=78000$

$\frac{31A}{9}+B=78000-\frac{7000}{3}$

$\frac{31A}{9}+B=\frac{227000}{3}$

$\frac{31A+9B}{9}=\frac{227000}{3}$

3(31A+9B)=9 X 227000

31A+9B=681000

0.22A+0.05B=4500 (Multiply by 9)

31A+9B=681000 (Multiply by 0.05)

1.98A+0.45B=40500

1.55A+0.45B=34050

Subtracting

0.43A=6450

A=$15000

From (III)

$C=\frac{22A}{9}+\frac{7000}{3}$

$C=\frac{22X15000}{9}+\frac{7000}{3} =39000$

C=$39000

from (I)

A+B+C=78000

15000+B+39000=78000

B=$24000

8 0

3 years ago

Please if you can? Thanks

irina [24]

Answer: 12 cm = x

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

Does anyone wanna join

Delvig [45]

Answer:

join what?

Step-by-step explanation:

7 0

3 years ago

\left(6x10^2\right)\div \left(3x10^{-5}\right)

Trava [24]

Answer:

$\frac{6\times 10^2}{3\times 10^{-5}}$ = 2 x 10⁷

Step-by-step explanation:

Given expression is $\frac{6\times 10^2}{3\times 10^{-5}}$

The given expression is simplified as follows;

$\frac{6\times 10^2}{3\times 10^{-5}} = (\frac{6}{3} )\times 10^{2-(-5)}\\\\(\frac{6}{3} )\times 10^{2-(-5)} = (\frac{6}{3} )\times 10^{2+5}\\\\(\frac{6}{3} )\times 10^{2+5} = 2 \ \times \ 10^7$

Therefore, the result of the given expression is 2 x 10⁷

6 0

3 years ago