given log_b a = c, which statement is true? (the b is subscript)
a. a = b^c
b. c = a^b
c. c = b^a
d. a = c^b
Well, if we have log_b a = c, then the correct statement is actually c = b^a. The logarithm of a to base b equals c means that b raised to the power of c gives us a, so in this case, c = b^a. So the correct answer is c. Remember, math can be quite confusing, but it's always important to log out of those worries!
The correct answer is d. a = c^b.
In the given problem, log_b a = c. This equation can be rearranged to express a in terms of c and b. Taking the base b to the power of both sides of the equation, we get:
b^(log_b a) = b^c.
Since b raised to the power of log_b a is equal to a (due to the definition of logarithms), the equation becomes:
a = b^c.
Hence, the correct statement is d. a = c^b.
To determine which statement is true, we need to rewrite the given equation using exponential notation. We have log_b a = c, which means b^c = a.
Now, let's evaluate each statement and see which one matches the given equation.
a. a = b^c
If we substitute the given equation, we have a = b^(log_b a). This statement is true based on the property that b^(log_b x) = x.
b. c = a^b
If we substitute the given equation, we have c = (log_b a)^b. This statement is not true because we don't have a property that directly relates logarithms to exponents in this way.
c. c = b^a
If we substitute the given equation, we have c = b^(log_b a). This statement is true based on the property that b^(log_b x) = x.
d. a = c^b
If we substitute the given equation, we have a = (log_b a)^b. This statement is not true because we don't have a property that directly relates logarithms to exponents in this way.
Based on the analysis, the true statements are:
a. a = b^c
c. c = b^a
Therefore, the correct answer is either a) or c).
or
remember this property:
the base of the logarithm is the base of your power.
I always made my students memorize this pattern
2^3 = 8 <------> log2 8 = 3
match it to your given question.