How to expand, then evaluate, and simplify this log question:
logbase7 (49( 3sqrt x^5))
I put the brackets in myself, I there were originally no brackets nor spaces in the question
log7 49(3√(x^5) )
= log749 + log73 + log7 x^(5/2)
= 2 + log7 3 + (5/2)log7 x
it can't be evaluated unless you give me a value for x
To expand, evaluate, and simplify the given logarithmic expression, you can follow these steps:
Step 1: Expand the expression inside the logarithm using the properties of logarithms.
First, we can rewrite the expression inside the logarithm as the product of two terms:
49(3√x^5) = 7^2 * (3√x^5)
Next, we can use the property of logarithms that states log_b(a * c) = log_b(a) + log_b(c) to expand the expression further:
log base 7 (49(3√x^5)) = log base 7 (7^2 * (3√x^5)) = log base 7 (7^2) + log base 7 (3√x^5)
Step 2: Simplify the expanded expression.
Since log base 7 (7^2) is equivalent to 2, and log base 7 (3√x^5) cannot be simplified further, the expression becomes:
2 + log base 7 (3√x^5)
Step 3: Evaluate the expression.
To evaluate the expression further, we need more information about the value of x. Without knowing x, we cannot determine the actual numeric value of the logarithm.
So, the final expression after expanding and simplifying is:
2 + log base 7 (3√x^5)