How good is it if I got a composite score of 25 on the ACT and I am only in 8th grade?

Solve for x if log 9 base x + log 3 base x^2 = 2.5

Y_Kistochka [10]

Not sure if the equation is

$\log_9x+\log_3(x^2)=\dfrac52$

or

$\log_x9+\log_{x^2}3=\dfrac52$

If it's the first one:

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot9^{\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot(3^2)^{\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{2\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^2)^2}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^4)}$

$9^{\log_9x+\log_3(x^2)}=x\cdot x^4$

$9^{\log_9x+\log_3(x^2)}=x^5$

On the other side of the equation, we'd get

$9^{5/2}=(3^2)^{5/2}=3^{2\cdot(5/2)}=3^5$

Then

$x^5=3^5\implies\boxed{x=3}$

If it's the second one instead, you can use the same strategy as above:

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot x^{\log_{x^2}3}$

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot\left((x^2)^{1/2}\right)^{\log_{x^2}3}$

(Note that this step assume $x>0$ )

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{(1/2)\log_{x^2}3}$

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{\log_{x^2}\sqrt3}$

$x^{\log_x9+\log_{x^2}3}=9\sqrt3$

Then we get

$9\sqrt3=x^{5/2}\implies x=(9\sqrt3)^{2/5}\implies\boxed{x=3}$

6 0

3 years ago

1/3(3+2x)−1=10 Drag and drop the statement that shows the solution to the equation into the box.

GarryVolchara [31]

Given
$\frac{1}{3}(3+2x)-1=10 \\ \\ \Rightarrow\frac{1}{3}(3+2x)=10+1=11 \\ \\ \Rightarrow3+2x=11\times3=33 \\ \\ \Rightarrow2x=33-3=30 \\ \\ \Rightarrow x= \frac{30}{2} =15$

Therefore, x = 15

5 0

3 years ago

Read 2 more answers

(3 + 8i) + (7 -- 2i) - (6 - 5i)<br> AO 4+1<br> B.O4 + 117<br> c. 16 +1<br> D.O4 + 1143

Lubov Fominskaja [6]

Answer: (3 + 8i) + (7 -- 2i) - (6 - 5i) = 4 + 15i

_____________________________________________

Simplify the expression.

4 + 15i

_____________________________________________

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3 0

3 years ago

Find a function that describes the sequence. Use y for the term in the sequence and n for its place in the list. Then use the fu

sammy [17]

B. y=n+20; 25,26,27 because if you plug in 1 into the equation it equals 21. 2+20=22, etc. so to find the next three terms of the equation plug in 5: y=5+20=25; plug in 6: y=6+20=26; and plug in 7: y=7+20=27

6 0

3 years ago

Gina will pay $14 for fabric at a crafting store. The tax rate is 8.5%. How much will she pay for her fabric including tax?

Gwar [14]

Answer:

$15.19

Step-by-step explanation:

8.5% = 0.085

0.085 x 14 = $1.19

1.19+14= $15.19

7 0

3 years ago