If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

To find the value of log5 512, we first need to express 512 and 5 in terms of base 2 or 3, since we know the logarithms of 2 and 3.

512 can be expressed as 2^9 and 5 can be expressed as 2^2.322 (since log2 5 = 2.322, calculated using the change of base formula and the given log values).

So, log5 512 = log(2^2.322) (2^9) = 9 / 2.322 = 3.876 approximately.

So, the value of log5 512 is approximately 3.876.

To find the value of log5 512, we first need to express 512 in terms of 5. We know that 512 = 2^9.

Now, we can use the change of base formula in logarithms, which states that logb a = logc a / logc b.

So, log5 512 = log 2^9 / log 5.

We can simplify this further using the power rule of logarithms, which states that logb a^n = n * logb a.

So, log5 512 = 9 * log 2 / log 5.

We know that log 2 = 0.3010 and log 5 = log (2*2 + 1) = log (4 + 1) = log 4 + log 1 = 2 * log 2 + log 1 = 2 * 0.3010 + 0 = 0.6020.

Substituting these values in, we get log5 512 = 9 * 0.3010 / 0.6020 = 4.5.

So, the value of log5 512 is 4.5.