Question

What is the solution to log 25x = 3?

Answer 1

Answer: x=40

Step-by-step explanation:

Answer 2

The solution to log (25x) = 3 is 40. This is calculated by using log rules.

What are the rules of a logarithmic function?

A function that has log terms is said to be a logarithmic function.

Some of the rules for solving log functions are as follows:

• The basic form of a logarithmic function is $log_b(m)=n$ ⇒ $m=b^n$.
• Product rule: $log_b(x)+log_b(y)=log_b(xy)$
• Quotient rule: $log_b(x)-log_b(y)=log_b(\frac{x}{y})$
• Power rule: $log_b(x)^n=nlog_b(x)$
• Identity rule: $log_b(b)=1$ where $(b^1=b)$

Finding the solution for the given function:

Given that,

log (25x) =3

Using basic form $log_b(m)=n$ ⇒ $m=b^n$

Here base b=10, m=25x and n=3

Then,

log (25x) =3

⇒ $25x = 10^3$

⇒ 25x = 1000

⇒ x = 1000/25

∴ x = 40.

Hence the solution of the given function is 40.

Learn more about logarithmic functions here:

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