How do you solve $5 {(2)}^{2 x} - 4 = 13$ $5(2)^(2x)-4=13$ ?

Question

1206 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-27T21:42:48

Please see the explanation.

Add 4 to both sides:

$5 {(2)}^{2 x} = 17$ $5(2)^(2x) = 17$

Divide both sides by 5:

${(2)}^{2 x} = \frac{17}{5}$ $(2)^(2x) = 17/5$

Use the natural logarithm on both sides:

$ln ({(2)}^{2 x}) = ln (\frac{17}{5})$ $ln((2)^(2x)) = ln(17/5)$

Use the property $ln (a^{b}) = (b) ln (a)$ $ln(a^b) = (b)ln(a)$

$(2 x) ln ((2)) = ln (\frac{17}{5})$ $(2x)ln((2)) = ln(17/5)$

Divide both sides by 2ln(x):

$x = \frac{ln (\frac{17}{5})}{2 ln (2)}$ $x = ln(17/5)/(2ln(2))$

check:

$5 {(2)}^{2 (\frac{ln (\frac{17}{5})}{2 ln (2)})} - 4 = 13$ $5(2)^(2(ln(17/5)/(2ln(2)))) - 4 = 13$

$5 {(2)}^{(\frac{ln (\frac{17}{5})}{ln (2)})} - 4 = 13$ $5(2)^((ln(17/5)/(ln(2)))) - 4 = 13$

$5 {(2)}^{({log}_{2} (\frac{17}{5})) - 4 = 13}$ $5(2)^((log_2(17/5)) - 4 = 13$

$5 (\frac{17}{5}) - 4 = 13$ $5(17/5) - 4 = 13$

$17 - 4 = 13$ $17 - 4 = 13$

$13 = 13$ $13 = 13$

$x = \frac{ln (\frac{17}{5})}{2 ln (2)}$ $x = ln(17/5)/(2ln(2))$ checks.

How do you solve 5(2)^(2x)-4=135(2)2x−4=135(2)^(2x)-4=13?