How do you solve $2^{x} = 4.5$ $2^x=4.5$ ?

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Answer 1 · 2016-07-22T07:43:34

$x = \frac{ln 4.5}{ln 2} \approx 2.17$ $x=(ln4.5)/(ln2) ~~ 2.17$

Take logs of both sides:

${ln 2}^{x} = ln 4.5$ $ln2^x = ln4.5$

Using power rule of logs, bring the x down in front

$x ln 2 = ln 4.5$ $xln2 = ln4.5$

Rearrange:

$x = \frac{ln 4.5}{ln 2}$ $x=(ln4.5)/(ln2)$

Answer 2 · 2016-07-22T07:43:59

$x = \frac{log 9}{log 2} - 1 = 2.16992500144$ $x=log 9/log 2-1=2.16992500144$

Given $2^{x} = 4.5$ $2^x=4.5$ , Find $x$ $x$

Solution:

$2^{x} = 4.5$ $2^x=4.5$

Take the logarithm of both sides of the equation

${log 2}^{x} = \frac{log 9}{2}$ $log 2^x=log 9/2$

$x \cdot log 2 = log 9 - log 2$ $x*log 2=log 9-log 2$

divide both sides of the equation by $log 2$ $log 2$

$\frac{x \cdot log 2}{log 2} = \frac{log 9 - log 2}{log 2}$ $(x*log 2)/log 2=(log 9-log 2)/log 2$

$(x*cancellog 2)/cancellog 2=(log 9-log 2)/log 2$

$x=log 9/log 2-1$

$x=2.16992500144$

God bless....I hope the explanation is useful.

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