Answer:
Option B is correct.
The value of x is -1.371(approximate)
Explanation:
Given equation: [tex]\log_5 15[/tex] =x+3
Using logarithmic rule:
[tex]\log_{10} (ab) =\log_{10} a +\log_{10} b[/tex]
[tex]\log_b b =1[/tex]
We can write [tex]\log_5 15[/tex] as;
[tex]\log_5 15 =\log_5 (5\times 3) = \log_5 5 +\log_5 3[/tex]
[tex]\log_5 15 = 1 +\log_5 3[/tex] [using logarithmic rule]
By graphing calculator the value of [tex]\log_5 3[/tex] = 0.682606194486.
then, we have
[tex]\log_5 15 = 1 +0.682606194486 =1.682606194486[/tex]
substitute this value in [1] to solve for x;
[tex]1.682606194486 =x+3[/tex]
Subtract 3 from both sides we have,
[tex]1.682606194486-3 =x+3-3[/tex]
Simplify:
-1.31739381 =x or
x =-1.317 (approx.)
Therefore, the approximate value of x is : -1.317
