Answer:
[tex]\sf x =15.5[/tex]
Step-by-step explanation:
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=5[/tex]
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=log_2 (32)[/tex]
[tex]\sf log_2\left\dfrac{(10x+5)}{5} =log_2 (32)[/tex]
[tex]\sf 2x+1 =32[/tex]
[tex]\sf 2x+1 -1=32-1[/tex]
[tex]\sf 2x =31[/tex]
[tex]\sf x =15.5[/tex]
Answer:
Step-by-step explanation:
[tex]log_{a}[/tex] [tex]x_{1}[/tex] - [tex]log_{a}[/tex] [tex]x_{2}[/tex] = [tex]log_{a}[/tex] [tex]\frac{x_{1} }{x_{2} }[/tex]
[tex]log_{a}[/tex] x = b ⇒ [tex]a^{b}[/tex] = x
~~~~~~~~~~~~~~
[tex]log_{2} (10x+5)[/tex] - [tex]log_{2} 5[/tex] = 5
[tex]log_{2} \frac{10x+5}{5}[/tex] = 5
[tex]\frac{10x+5}{5}[/tex] = [tex]2^{5}[/tex]
10x + 5 = 32 × 5
2x + 1 = 32
x = 15.5
