MATHEMATICS HIGH SCHOOL

What is the solution of log3x − 5 16 = 2?

the base is 3x - 5, and the argument is 16

Answers

Answer 1

Answer:

Answer:

x=3

Step-by-step explanation:

The given equation is $\log_(3x-5)16=2$

The relation between logarithmic function and exponential function is given by

$\text{If }y=b^x\text{ then }x=\log_b(y)$

On comparing, we get

b = 3x-5

y = 16

x = 2

Hence, using the relation, we have

$16=(3x-5)^2$

Take square root both sides

$\pm√(16)=3x-5$

On simplifying

$3x-5=\pm4\n\n3x=\pm4+5\n\nx=(1)/(3)(5\pm4)\n\nx=(1)/(3)*1,(1)/(3)*9\n\nx=(1)/(3),3$

For x = 1/3

$3x-5\n\n=3\cdot (1)/(3)-5\n\n=-4$

Base cannot be negative.

Hence, the value of x is 3

Answer 2

Answer: Hello,

log (16)=2 in base 3x-5
==>16=2^(3x-5)
==>2^4=2^(3x-5)
==>4=3x-5
==>3x=9
==>x=3

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