Question

If log2 X + log4 X = 5, find X for the 3 decimal places.

Answer 1

Answer:

$x=32768.000$

Step-by-step explanation:

One is given the following expression:

$log_2(x)+log_4(x)=5$

Use the logarithm base change rule, which states the following:

$log_b(y)=\frac{log(y)}{log(b)}$

Remember, a logarithm with not base indicated is another way of writing a logarithm to the base of (10). One can apply the base change rule to this situation:

$log_2(x)+log_4(x)=5$

$\frac{log(x)}{log(2)}+\frac{log(x)}{log(4)}=5$

Factor out (log(x)),

$(log(x))(\frac{1}{log(2)}+\frac{1}{log(4)})=5$

Inverse operations:

$log(x)=\frac{5}{\frac{1}{(log(2)+log(4)}}$

Simplify,

$log(x)=5(log(2)+log(4))$

$log(x)=4.51545$

Now rewrite the logarithm, remember, a logarithm is another way of writing an exponent, in the following format:

$b^x=y\ \ -> log_b(y)=x$

$log(x)=4.51545$

$10^4^.^5^1^5^4^5=x$

$32768.000=x$