1.318
Explanation:
Really what you're looking for is a value of x that, when 7 is raised to that power, will give you 13.
putting the equation in terms of f and g (any variables will do) :
7^x = f(x)
13= g(x)
using the rule if f(x)=g(x) then ln f(x) = ln g(x)
If any function f of x equals g of x then the natural log of f of x equals the natural log of g of x.
Therefore:
ln (7^x) = ln (13)
With logs, if there is something raised a power, the exponent can simply be moved to the front, so:
ln (7^x) = x * ln 7
note: *=multiplication
therefore your new equation is
x*ln 7 = ln 13
if you divide both sides by ln 7, you get that
[tex]x = \frac{ln 13}{ln 7} [/tex]
x = 1.318123223
but you only need four sig figs (significant figures) so your answer is
x = 1.318
*Note = the answer is 1.318 only because those are the first four digits of the answer. I suggest looking up rules for sig figs if you do not know what they already are
HOPE THAT HELPS
_V :)
