6. Solving Exponential and Logarithmic Equations
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If two equivalent logarithmic expressions have the same base, then the arguments must be equal.
x=4
log_2(m) + log_2(n)=log_2(mn)
m=log_2(2^m)
Calculate power
Equate arguments
Distribute x
LHS-8=RHS-8
Rewrite -2x as 2x-4x
Factor out x
Factor out -4
Factor out (x+2)
Use the Zero Product Property
(I): LHS-2=RHS-2
(II): LHS+4=RHS+4
x= -2
Subtract term
x= 4
Subtract term
log_2(2) = 1
Calculate logarithm
Add terms