Question 201513
I assume the problem is to solve: {{{7^(x+2) - 4 = 136}}}<br>
To start with, add 4 to both sides giving
{{{7^(x+2) = 140}}}
Next, since 140 is not a power of 7 (it is a multiple but not a power), we will need to use logarithms. Use base 10 logarithms or natural logarithms, it doesn't matter. I will use base 10:
{{{log((7^(x+2))) = log((140))}}}
The {{{log(140)}}} is approximately 2.146128 so now we have
{{{log((7^(x+2))) = 2.146128}}}
Using a property of logarithms ({{{log((a^b)) = b*log((a))}}}) we get
{{{(x+2)*log((7)) = 2.146128}}}
Dividing by log(7) we get
{{{x+2 = 2.146128/(log((7)))}}}
The log(7) is approximately 0.845098 giving us
{{{x + 2 = 2.146128/0.845098 = 2.539501}}}
Subtracting 2 from both sides we get (rounded to the nearest hundredth):
x = 0.56