Question

How would I solve this problem?
log2^x + log2^5 = 4

Answer 1

Adding the logarithms of two quantities is equivalent to taking the logarithm of their product.

\[\log a + \log b = \log (a*b)\]

Answer 2

Do we know the base of the log here? I'm wondering if this is really
\[\log 2^x\] or maybe \[\log_{2}x\]

Answer 3

It's the second option.

Answer 4

ah, yes, that makes a big difference :-)

Answer 5

My first statement still holds, so we would have
\[\log_{2}x + \log_{2}5 = 4\]\[\log_{2}(5x) = 4\]Raise the log base to each side to eliminate the log and we haev
\[2^{\log_{2}{5x}} = 2^4\]\[5x=2^4\]

Answer 6

that ^ in the problem statement threw us off! :-)

Answer 7

if you had written log2 x + log2 5 = 4 I would have understood you meant the log base 2, but this looked like you really meant 2^x and 2^5.

not too hard to solve the other version (assume base 10 for the log)

\[\log 2^x + \log 2^5 = 4\]\[\log {2^{x+5}} = 4\]Raise base to both sides
\[2^{x+5} = 10^4\]Now take log base 2 of both sides
\[x+5 = \log_{2}10^4\]\[x = \log_{2}10^4 - 5 \approx 8.28771\]

Answer 8

Thank you. c: