All categories

2 years ago

Solve the exponential equation. (logs) 3(1.05)^x+1=6

1 answer:

8 0

$\bf 3(1.05)^x+1=6\implies 3(1.05)^x=5\implies (1.05)^x=\cfrac{5}{3}\\\\
-----------------------------\\\\
log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\qquad thus\\\\
-----------------------------\\\\
log\left[ (1.05)^x \right]=log\left( \cfrac{5}{3} \right)\implies xlog\left[ (1.05) \right]=log\left( \cfrac{5}{3} \right)
\\\\\\
x=\cfrac{log\left( \frac{5}{3} \right)}{log(1.05)}$

You might be interested in

If you multiply by 3 negatives does it equal a negative?

qwelly [4]

Yes it does because when u multiply 2 negative you get a positive but since your adding another negative it goes back to a negative

6 0

3 years ago

You deposit $10,000 in a money-market account that pays an annual interest rate of 4.4%. The interest is compounded quarterly. H

sergiy2304 [10]

Total = principal * (1 + rate/n)^n*years
where "n" is the number of compounding periods per year
Total = 10,000 * (1 + .044/4)^4*2
Total = 10,000 * (1.011)^8
Total = 10,000 * 1.0914635699 
Total = 10,914.64

3 0

3 years ago

Order these ratios from least to greatest- 7:2, 12 to 4, 20/6, 21:14, 10:5 pls :,)

Brrunno [24]

Answer:

21:14, 10:5, 12 to 4, 20/6, and 7:2

Step-by-step explanation:

first simplify all the ratios.

the first one is already simplified

12 to 4 = 3 to 1

20/6 = 10/3

21:14 = 3:2

10:5 = 2:1

Next find the least common factor the the three digits, 1, 2, and 3 and which is 6.

Multiply the simplified factors into the least common factor. So 7:2 will be multiplied by 6 so it will be 21:6

Do it with the rest of the factors and get

21:6, 18 to 6, 20/6, 9:6, and 12:6

Finally order them from least to greatest,

9:6, 12:6, 18 to 6, 20/6, and 21:6

21:14, 10:5, 12 to 4, 20/6, and 7:2

4 0

2 years ago

Iluguru sold an artick to bol to gain 20% Thereafteru

Anastasy [175]

Answer: £5

Step-by-step explanation:

Bole sold the article for 125% while he bought it for 100%.

Bole sold for £7.50 so £7.50=125%

£7.50/1.25=£6

125%/1.25=100%

£6=100% (the cost Bole bought the article with from Iluguru)

Iluguru sold it at 120% so 120% is £6

To find 100% we divide by 1.2

£6/1.2=£5

Iluguru bought article for £5 originally

8 0

2 years ago

Find the smallest possible solution to 2/3x^2=24

Bezzdna [24]

$\dfrac{2}{3} x^2 = 24$

---------------------------------------------------------------------
Divide by 2/3 on both sides :
---------------------------------------------------------------------
$x^2 = 24 \div \dfrac{2}{3}$

---------------------------------------------------------------------
Change the divide fraction to multiplication fraction :
---------------------------------------------------------------------
$x^2 = 24 \times \dfrac{3}{2}$

---------------------------------------------------------------------
Simplify :
---------------------------------------------------------------------
$x^2 = 36$

---------------------------------------------------------------------
Square root both sides :
---------------------------------------------------------------------
$x = \pm \sqrt{36}$

---------------------------------------------------------------------
Answer :
---------------------------------------------------------------------
$x = \pm6$

---------------------------------------------------------------------
Answer: The smallest possible value of x is -6
---------------------------------------------------------------------

4 0

3 years ago