michaeladdy49p98i1r
Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Find the value of x which satisfies the following equation.
log2(x−1)+log2(x+5)=4

Find The Value Of X Which Satisfies The Following Equation Log2x1log2x54 class=

Sagot :

AǫᴜᴀWɪᴢ

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x = 3[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: log_{2}(x - 1) log_{2}(x + 5) = 4[/tex]

[tex]\qquad \tt \rightarrow \: log_{2} \{(x - 1)(x + 5) \} = 4[/tex]

[ log (x) + log (y) = log (xy) ]

[tex]\qquad \tt \rightarrow \: ( x - 1)(x + 5) = {2}^{4} [/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 5x - x - 5 = 16[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x - 5 - 16 = 0[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x -21 = 0[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 3x - 21 = 0[/tex]

[tex]\qquad \tt \rightarrow \: x(x + 7) - 3(x + 7) = 0[/tex]

[tex]\qquad \tt \rightarrow \: (x + 7)(x - 3) = 0[/tex]

[tex]\qquad \tt \rightarrow \: x = - 7 \: \: or \: \: x = 3[/tex]

The only possible value of x is 3, since we can't operate logarithm with a negative integer in it.

[tex]\qquad \tt \rightarrow \: x = 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.