Which logarithmic equation is equivalent to L^m = E
1) LogL E = m
2) logE L = m
3) logm E= L
4) logE m= L
1) LogL E = m
LogE l=m
To determine which logarithmic equation is equivalent to L^m = E, we need to understand the properties of logarithms.
The logarithm of a number is the exponent to which another fixed value, called the base, must be raised to produce that number. In this case, we have L^m = E, where L is the base, m is the exponent, and E is the result.
Now, let's go through the options one by one:
1) LogL E = m
This equation suggests that taking the logarithm of E with base L will give us m. However, in the original equation L^m = E, L is the base and m is the exponent. This option has the variables mixed up, so it is not equivalent.
2) logE L = m
This equation suggests that taking the logarithm of L with base E will give us m. In the original equation L^m = E, L is the base and m is the exponent. This option also has the variables switched, so it is not equivalent either.
3) logm E = L
This equation suggests that taking the logarithm of E with base m will give us L. In the original equation L^m = E, L is the base and m is the exponent. This option correctly identifies the base as E and the exponent as L, so it is not equivalent either.
4) logE m = L
This equation suggests that taking the logarithm of m with base E will give us L. In the original equation L^m = E, L is the base and m is the exponent. This option correctly identifies the base as E and the exponent as L. Therefore, this option is the correct choice and is equivalent to the original equation L^m = E.
So, the correct answer is option 4) logE m = L.
I had my students memorize this pattern
2^3 = 8 <-----> log2 8 = 3
That way you can tell which parts go where.
What do you think?