How to do this logs question?

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Answer 1 · 2018-03-01T04:46:57

$a = 2, b = 4$ $a=2 , b=4$

$y = a {log}_{2} x + b$ $y=a log_2 x+b$

So this must pass through $(8, 10), (14, 32)$ $(8,10),(14,32)$

So in the equation put $y = 10, x = 8$ $y=10,x=8$

$10 = a {log}_{2} 8 + b$ $10=alog_2 8+b$

$10 = a \cdot 3 + b ({log}_{2} 8 = 3)$ $10=a*3+b " " (log_2 8= 3)$

Now put $y = 14, x = 32$ $y=14,x=32$

$14 = a {log}_{2} 32 + b$ $14=a log_2 32+b$

$14 = a \cdot 5 + b$ $14=a*5+b$ ${log}_{2} 32 = 5$ $log_2 32=5$

$14 = 3 \cdot a + b + 2 \cdot a$ $14=3*a+b+2*a$

$14 = 10 + 2 \cdot a$ $14=10+2*a$

$4 = 2 \cdot a$ $4=2*a$

$2 = a$ $2=a$

$10 = 3 \cdot 2 + b$ $10=3*2+b$

$10 - 6 = b$ $10-6=b$

$b = 4$ $b=4$

Answers $a = 2, b = 4$ $a=2, b=4$