Answer:
x = -8 , x = 5
Step-by-step explanation:
Applying logarithmic rule
[tex]log_{a}b = x\\b = a^{x}[/tex]
If a > 0 and a ≠ 1 then logarithm of a positive number b is defined as b equal to a raised to x
[tex]2=\log _7(x^2+3x+9)\\7^{2} = x^2+3x+9\\49=x^2+3x+9\\x^2+3x+9- 49 = 0\\x^2+3x-40 = 0\\\text {Factor completely}\\(x+8)(x-5) = 0[/tex]
Equating to zero
x+8 = 0 ; x - 5 =0
x = -8 ; x = 5
Therefore the answer is x = -8 , x = 5
Checking
Substituting x = -8
[tex]2=\log _7(64-24+9) \\2=2[/tex]
Substituting the value of x = 5
[tex]2=\log _7(25+15+9) \\2=2[/tex]
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