How do I solve this? Thank you!

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Answer 1 · 2016-11-08T17:42:38

$x = 2^{13} = 8, 192$ $x= 2^13 = 8,192$

The logs are all to the same base.

$5 {log}_{2} 4 + {log}_{2} 8 = {log}_{2} x \leftarrow$ $color(blue)(5)log_2 4 +log_2 8 = log_2 x" "larr$ use the power law

${log}_{2} 4^{5} + {log}_{2} 8 = {log}_{2} x$ $log_2 4^color(blue)(5) +log_2 8 = log_2 x$

If logs are being added, numbers are multiplied...

${log}_{2} (4^{5} \times 8) = {log}_{2} x \leftarrow$ $log_2 (4^5 xx 8) = log_2 x" "larr$ change to powers of 2

${log}_{2} ({(2^{2})}^{5} \times 2^{3}) = {log}_{2} x$ $log_2 ((2^2)^5 xx 2^3) = log_2 x$

${log}_{2} (2^{10} \times 2^{3}) = {log}_{2} x$ $log_2 (2^10 xx 2^3) = log_2 x$

${log}_{a} B = {log}_{a} C \Leftrightarrow B = C$ $log_a B = log_a C hArr B=C$

$2^{13} = x$ $2^13 =x$