Solve log 4x + log 13 = 0. Round to the nearest thousandth if necessary

in log form, 2^10 = 1024 is:  log(to the base 2) 1024 = 10

When you multiply two numbers with the same base, you add their exponents.

Logs are exponents, so the reason that they're added is to get the answer to a multiplication problem.

So, working backwards, log(4x) + log(13)  =  log(4x·13)  =  log(52x)

Since the problem says that log(52x)  =  0, changing it back into eponential form:  10^0  =  52x

--->  1  =  52x

--->  x  =  1/52

Which is the logarithmic form of 2¹⁰ = 1024?