Question

For which value of p which satisfies the relation log2(x-1) + 2 =log2(3p+1)

Answer 1

Answer:

The value of p is 5

Step-by-step explanation:

Formula:

log (M/N) = logM - logN

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Answer 2

Answer:

$p=\frac{1}{3}(4x-5)$

Step-by-step explanation:

The given logarithmic equation is

$\log_2(x-1)+2=\log_2(3p+1)$

Take the log terms to one side of the equation

$\log_2(x-1)-\log_2(3p+1)=-2$

Apply the quotient rule of logarithm $\log(a/b)=\log a-\log b$

$\log_2\left( \frac{x-1}{3p+1}\right )=-2$

Now apply the rule: $log_bx=a\Rightarrow x=b^a$

$\frac{x-1}{3p+1)}=2^{-2}$

Solving the equation for p

$\frac{(x-1)}{(3p+1)}=\frac{1}{4}\\\\3p+1=4x-4\\\\3p=4x-5\\\\p=\frac{1}{3}(4x-5)$

Thus, the value of p is

$p=\frac{1}{3}(4x-5)$