Question 83403
I am assuing that you probably mean this for the equation:
{{{7^(x + 8) = 38}}}


Take the ln or the log of each side, whichever you prefer.

{{{ln 7^(x+8) = ln 38 }}}


By law of logarithms, 
{{{(x+8) ln 7 = ln 38 }}}


By distributive property:
{{{x ln 7 + 8 ln 7 = ln 38 }}}
{{{x ln 7 = ln 38 - 8 ln 7 }}}


Divide by ln 7:
{{{x= (ln 38 - 8 ln 7)/(ln 7) }}}


Using a calculator, you should have 
{{{x= -6.1306}}} which of course rounds off to {{{x=-6.13}}}


You may want to see my Lesson Plans on Logarithms in algebra.com.  Also, check out my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, and look for "MATH IN LIVING COLOR", then look in College Algebra.  My entire Chapter 4 of College Algebra is devoted to LOGARITHMS.


R^2 at SCC