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
