Given:
15. 
17. 
19. 
To find:
The values of the given logarithms by using the properties of logarithms.
Solution:
15. We have,

Using property of logarithms, we get
![[\because \log_aa=1]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Clog_aa%3D1%5D)
Therefore, the value of
is 1.
17. We have,

Using properties of logarithms, we get
![[\because \log_a\dfrac{m}{n}=-\log_a\dfrac{n}{m}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Clog_a%5Cdfrac%7Bm%7D%7Bn%7D%3D-%5Clog_a%5Cdfrac%7Bn%7D%7Bm%7D%5D)
![[\because \log_aa=1]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Clog_aa%3D1%5D)
Therefore, the value of
is -1.
19. We have,

Using property of logarithms, we get
![[\because a^{\log_ax}=x]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5E%7B%5Clog_ax%7D%3Dx%5D)
Therefore, the value of
is 100.
Answer:
$7,440.
Step-by-step explanation:
We have been given the tax rates as follows:
$0-$11,000 = No tax.
$11,000-$43,000 = 20%.
$43,000-$150,000 = 40%.
Earnings over $150,000 = 45%.
Since last year Carys earned $45,600, so we will have to find the tax paid by her for 11,000-43,000 at rate of 20%, then the tax for amount over 43,000 at the rate of 40%.





Therefore, Carys paid an amount of $7,440 in tax.
Answer:
i think 41.3
Step-by-step explanation: