Is the following correct when restating logs with variables to exponential?
Log:
log_a(a^3) --- base = a
Exp:
a^3 = a
I know when dealing with real numbers, this is what you do:
Log:
log(10^5)
Exp:
10^5 = 100 000
I am uncertain what your question is.
loga (a^3)= 3loga a= 3*1=3
No, the restatement of the logarithm is not correct in both cases.
Let's break down each situation:
1. For the logarithm example: log_a(a^3) with base a.
To restate this logarithm as an exponential equation, you need to remember the basic relationship between logarithms and exponentials. In general, log_a(b) = x can be restated as a^x = b. Applying this to the given example, we have:
log_a(a^3) = x
Thus, according to the restatement rule, we get:
a^x = a^3
Note that the exponent on the left side of the equation equates to the exponent on the right side. However, since the base is not matching, the equation should be written as:
a^x ≠ a^3
So the correct restatement for this logarithm is: a^x ≠ a^3
2. For the exponential example: 10^5 = 100,000.
Here, you have correctly restated the exponential equation. The exponent of 5 tells you how many times to multiply 10 by itself. So, in this case, raising 10 to the power of 5 gives you the value of 100,000. Therefore, the correct restatement is:
10^5 = 100,000
Remember, when restating logarithms as exponentials, the base of the logarithm becomes the base of the exponential, and the logarithm's argument (inside the parentheses) becomes the value raised to the power.