Answer:
B. [tex]\log_{7} 149+2 = x[/tex]
Step-by-step explanation:
Let [tex]7^{x-2} = 149[/tex], we proceed to find its equivalent expression by applying logarithm properties:
1) [tex]7^{x-2} = 149[/tex] Given.
2) [tex]\log_{7} 7^{x-2} = \log_{7} 149[/tex] Definition of logarithm.
3) [tex](x-2)\cdot \log_{7}7 = \log_{7} 149[/tex] [tex]\log_{a} b^{c} = c\cdot \log_{a} b[/tex]
4) [tex]x-2=\log_{7}149[/tex] [tex]\log_{a}a = 1[/tex]
5) [tex]x = \log_{7}149+2[/tex] Compatibility with addition/Existence of additive inverse/Modulative property
6) [tex]\log_{7} 149+2 = x[/tex] Symmetrical property/Result.
Hence, the right answer is B.
