Elsa's claim that the logarithmic equation [tex]\log_2(x) = \log_2(3x+5)+4[/tex] has no solution is true
The logarithmic equation is given as:
[tex]\log_2(x) = \log_2(3x+5)+4[/tex]
Express 4 as a logarithm expression
[tex]\log_2(x) = \log_2(3x+5)+\log_2(16)[/tex]
Apply the rule of logarithm
[tex]\log_2(x) = \log_2(16 *(3x+5))[/tex]
Cancel out the common base
x = 16 *(3x+5)
Expand
x = 48x + 80
Collect like terms
x - 48x = 80
This gives
-47x = 80
Divide both sides by -47
x =-80/47
When the value of x is negative, then the logarithmic equation has no solution
Hence, Elsa's claim is true
Read more about logarithmic equations at:
https://brainly.com/question/237321
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