log5(1+.03%)

To simplify the expression log5(1+.03%), we first need to understand the properties of logarithms.

The logarithm with base "b" of a number "x" is defined as the power to which "b" must be raised to obtain "x". In our case, we have a logarithm with base 5, so log5(x) = y can be rewritten as 5^y = x.

Now, let's solve log5(1+.03%) step by step:

1. Convert the percentage into a decimal: 0.03% = 0.03/100 = 0.0003.
2. Add 1 to the decimal: 1 + 0.0003 = 1.0003.
3. Apply the logarithm with base 5 to 1.0003: log5(1.0003).

At this point, we can't provide an exact numerical value for log5(1.0003) without using a calculator or any other computational tool. However, we can use an approximation:

4. Rewrite 1.0003 as a power of 5: 1.0003 ≈ 5^a.
5. Take the logarithm of both sides with base 5: log5(1.0003) ≈ log5(5^a).

Since log5(5^a) simplifies to just "a", we have:
log5(1.0003) ≈ a.

So, the logarithm log5(1+.03%) is approximately equal to "a" or the exponent needed to obtain 1.0003 from 5. To get the exact numerical value, you can use a calculator or a math software program.