Question

Elsa tries to solve the following equation, and determines there is no solution. is she correct? explain. log2x = log2(3x 5) 4

Answer 1

Elsa's claim that the logarithmic equation $\log_2(x) = \log_2(3x+5)+4$ has no solution is true

How to determine the true statement?

The logarithmic equation is given as:

$\log_2(x) = \log_2(3x+5)+4$

Express 4 as a logarithm expression

$\log_2(x) = \log_2(3x+5)+\log_2(16)$

Apply the rule of logarithm

$\log_2(x) = \log_2(16 *(3x+5))$

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:

brainly.com/question/237321

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