Question

Solve: log5x3 - logx2 = 2

Answer 1

log 5x³-log x²=2
Log A-log B=log A/B
log 100=2      (⇔10²=100)

log (5x³/x²)=log 100
log 5x=log 100

Then:
5x=100
x=100/5
x=20

Answer: x=20.

Answer 2

The value of x is 20 in the logarithm equation log5x³ - logx² = 2 after applying the property of log.

What is a logarithm?

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

$\rm a^b = c\\log_ac =b$

We have:

$\rm log5x^3 - logx^2 = 2$

From the property of division of log:

log(5x³/x²) = 2

Since, x ≠ 0

log(5x) = 2

5x = 10²  (removing log)

x = 20

Thus, the value of x is 20 in the logarithm equation log5x³ - logx² = 2 after applying the property of log.

Learn more about the Logarithm here:

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