Use the change-of-basis identity,

to write

Use the product-to-sum identity,

to write

Redistribute the factors on the left side as

and simplify to

Now expand the right side:

Simplify and rewrite using the logarithm properties mentioned earlier.





(C)
Answer:
b = 6.79
Step-by-step explanation:
Data provided:
logb(5) = 0.84
Now,
From the properties of log function
logₓ (z)=
(where the base of the log is equal for both numerator and the denominator)
also,
log(xⁿ) = n × log(x)
thus,
using the above properties, we can deduce the results as:
logₓ(y) = n is equivalent to y = xⁿ
Thus,
logb(5) = 0.84
⇒
= 0.84
or
log(5) = 0.84 × log(b)
or
log(5) =
(as log(xⁿ) = n × log(x) )
taking the anti-log both sides
we get
5 =
or
b = 6.79
I am attaching an image with the two solutions represented by the blue areas highlighted in your original graphs. Let me know if you have questions.
Selling Price = $145
Charge on first $25 is 5.25%
5.25% of $25 =

Charge on rest is 3.25%
rest amount = $145 - $25 = $120
3.25% of $120 =
