What is the value of x? 38 21 21 Drawing not to scale

Condense the following logs into a single log:

mamaluj [8]

QUESTION 1

The given logarithm is

$8\log_g(x)+5\log_g(y)$

We apply the power rule of logarithms; $n\log_a(m)=\log_(m^n)$

$=\log_g(x^8)+\log_g(y^5)$

We now apply the product rule of logarithm;

$\log_a(m)+\log_a(n)=\log_a(mn)$

$=\log_g(x^8y^5)$

QUESTION 2

The given logarithm is

$8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)$

We apply the power rule of logarithm to get;

$=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)$

We apply the product to obtain;

$=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)$

We apply the quotient rule; $\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )$

$=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})$

$=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})$

7 0

2 years ago

Solve question 20 (a) and (b)

RUDIKE [14]

Answer:

You first have to read on the coordinates where the curve and the straight line meet or cuts across

a.) 53

b.) 13

5 0

2 years ago

In the triangle shown we can find the angle θ as follows calculator

Xelga [282]

Given a right triangle with hypothenus of measure 34, the side opposite the angle θ of measure 30, and the side adjacent the angle theta of measure 16.

$\sin\theta= \frac{opposite}{hypothenuse} = \frac{30}{34} = \frac{15}{17} \\ \\ \Rightarrow \theta=\sin^{-1}\left( \frac{15}{17} \right) \\ \\ \\ \cos\theta= \frac{adjacent}{hypothenuse} = \frac{16}{34} = \frac{8}{17} \\ \\ \Rightarrow \theta=\cos^{-1}\left( \frac{8}{17} \right) \\ \\ \\ \tan\theta= \frac{opposite}{adjacent} = \frac{30}{16} = \frac{15}{8} \\ \\ \Rightarrow \theta=\cos^{-1}\left( \frac{15}{8} \right)$

3 0

2 years ago

In a recent year, 22 percent of email users said they spend less time using email because of spam. what fraction of email users

Alchen [17]

Remember, percent is always out of 100. If you have 22%, you have 22 people per every 100 people, or, 22/100.

22/100 is the incomplete answer because it needs to be simplified. If you divide both numbers by two you get 11/50 which is the lowest fraction you can have because 11 is a prime number.

5 0

2 years ago

Elijah and Riley are playing a board game. Elijah chooses the dragon for his game piece, and Riley chooses the cat for hers. The

IgorLugansk [536]

Answer: 3/8

Step-by-step explanation: 7/8 - 1/2= (7*2)-(1*8)

--------------- = 6/16 6 divided by 2 and then 16 divided by 2= 3/8

^8*2

5 0

2 years ago