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You were done at log40/log4. That’s the answer. Anything else is just a decimal approximation.
Log 4 is not equal to 0.602
4^x = 40ln(4^x) = ln40xln(2^2) = ln402xln2 = ln40x = ln40 / 2ln2
xlog4 = log40X = log4 + log10 / log4X = 1 + log10/log4X ≈ 1+1,6609640X ≈ 2,6609640
You were done at log40/log4. That’s the answer. Anything else is just a decimal approximation.
Log 4 is not equal to 0.602
4^x = 40
ln(4^x) = ln40
xln(2^2) = ln40
2xln2 = ln40
x = ln40 / 2ln2
xlog4 = log40
X = log4 + log10 / log4
X = 1 + log10/log4
X ≈ 1+1,6609640
X ≈ 2,6609640