.
(a) x- intercept
To find x-intercept, we should solve this equation
H(x) = 0, or = 0.
For any base logarithm, b, if = 0, then a= 1.
In our case, it gives x+8 = 1, which implies x= 1 - 8 = -7. ANSWER
(b) y- intercept
To find y-intercept, we should calculate H(0), placing x= 0:
H(0) = = = 3. ANSWER
At this point, the problem is just solved in full.
Solved.
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It is not necessary to make change the logarithm base, as the other tutor does.
In opposite, it is simpler and it is MORE CORRECT WAY to complete the solution without changing the logarithm base.
Warning: if in this problem you will make change of the logarithm base,
your teacher will conclude immediately that you do not know basics of logarithms.
On logarithms and their properties, see these introductory lessons
- WHAT IS the logarithm
- Properties of the logarithm
- Change of Base Formula for logarithms
- Evaluate logarithms without using a calculator
- Simplifying expressions with logarithms
in this site.