Question

can anyone solve this for me​

Answer 1

Answer:

$\boxed{\boxed{\huge{\pink{x = 5}}}}$

Step-by-step explanation:

$\bold{\underline{\red{Given}}}\longrightarrow \\ log_{4}(8) + log_{4}(x + 3) - log_{4}(x - 1) = 2$

$\bold{\underline{\blue{To \: find}}} \\ value \: of \: x$

$\bold{\underline{\green{Concept \: used}}}\longrightarrow \\ logm + logn = logmn \\ logm - logn = log \dfrac{m}{n} \\ log_{m}(x) = n \: = > x = {m}^{n}$

$\bold{\underline{\pink{Solution}}}\longrightarrow \\ log_{4}(8) + log_{4}(x + 3) - log_{4}(x - 1) = 2$

$= > log_{4}(8(x + 3) ) \: \: - log_{4}(x - 1) = 2 \\ = > log_{4}(8x + 24) - log_{4}(x - 1) = 2 \\ = > log_{4}( \dfrac{8x + 24}{x - 1} ) = 2 \\ = > ( \dfrac{8x + 24}{x - 1} ) = {4}^{2} \\ = > 8x + 24 = 16 \: (x - 1) \\ = > 8x + 24 = 16x - 16 \\ = > 16 + 24 = 16x - 8x \\ = > 8x = 40 \\ = > x = \dfrac{40}{8} \\ = > x = 5$