Question 216482
{{{8^(1.044x + 1) = 14}}}
<pre><font size = 4 color = "indigo"><b>
take natural logs of both sides

{{{ln(8^(1.044x + 1)) = ln(14)}}}

Bring the exponent in front of the natural log:

{{{(1.044x + 1)ln(8) = ln(14)}}}

Divide both sides by {{{ln(8)}}}

{{{((1.044x + 1)ln(8))/ln(8) = ln(14)/ln(8)}}}

{{{((1.044x + 1)cross(ln(8)))/cross(ln(8)) = ln(14)/ln(8)}}}

{{{1.044x + 1 = ln(14)/ln(8)}}}

{{{1.044x = ln(14)/ln(8)-1}}}

Divide both sidesa by {{{1.044}}}

{{{(1.044x)/1.044 = (ln(14)/ln(8)-1)/1.044}}}

{{{(cross(1.044)x)/cross(1.044) = (ln(14)/ln(8)-1)/1.044}}}

{{{x = (ln(14)/ln(8)-1)/1.044}}}

From calculator:

{{{x = 0.2577761565}}}

Rounded to four decimal places:

{{{x=0.2578}}}

Edwin</pre></font></b>