Question

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

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

Answer 1

Hello,

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

Answer 2

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

$\pm\sqrt{16}=3x-5$

On simplifying

$3x-5=\pm4\\\\3x=\pm4+5\\\\x=\frac{1}{3}(5\pm4)\\\\x=\frac{1}{3}\times1,\frac{1}{3}\times9\\\\x=\frac{1}{3},3$

For x = 1/3

$3x-5\\\\=3\cdot \frac{1}{3}-5\\\\=-4$

Base cannot be negative.

Hence, the value of x is 3