Solve the equation log 749 2x 1 The solution set is Type

Solve the equation. log 7_49 = 2x + 1 The solution set is { }. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Solution

log₇49 = log₇(7²)

since log(aⁿ) = nlog(a)

log₇49 = log₇(7²) = 2log₇(7)

since log_a(aⁿ) =1

log₇49 = log₇(7²) = 2log₇(7) = 2(1)=2

but given log₇49 = 2x+1

so 2x+1=2

2x=2-1

2x=1

x=1/2