Question 112248
Please help me solve this equation: 
3^0.16x=1.5 
i've tried to take logs of both sides but it doesn't come out with the right answer. 
Thanks in advance!

<pre><font face = "book antiqua" size = 5><b>
{{{3^(0.16x)}}} = {{{1.5}}}

Take the log<sub>10</sub> of both sides:

{{{log(10,3^(0.16x))}}} = {{{log(10,1.5)}}}  

Move the exponent 0.16x out in front of the
log as a coefficient.

{{{0.16x*log(10,3)}}} = {{{log(10,1.5)}}}

Divide both sides by {{{0.16*log(10,3)}}}

{{{(0.16x*log(10,3))/(0.16*log(10,3))}}} = {{{(log(10,1.5))/(0.16*log(10,3))}}}

{{{x}}} = {{{(log(10,1.5))/(0.16*log(10,3))}}}

{{{x}}} = {{{0.1760912/(0.16*0.4771212547)}}}

{{{x}}} = {{{2.30668904}}}

------------------------------

You can also do it by taking the natural log
of both sides instead of the log<sub>10</sub>:

{{{3^(0.16x)}}} = {{{1.5}}}

Take the ln of both sides:

{{{ln(3^(0.16x))}}} = {{{ln(1.5)}}}  

Move the exponent 0.16x out in front of the
ln as a coefficient.

{{{0.16x*ln(3)}}} = {{{ln(1.5)}}}

Divide both sides by {{{0.16*ln(3)}}}

{{{(0.16x*ln(3))/(0.16*ln(3))}}} = {{{(ln(1.5))/(0.16*ln(3))}}}

{{{x}}} = {{{(ln(1.5))/(0.16*ln(3))}}}

{{{x}}} = {{{0.4054651081/(0.16*1.098612289)}}}

{{{x}}} = {{{2.30668904}}}

Edwin</pre></font>