Expand the Logarithmic Expression log base 4 of square root of 10x

Problem

(log_4)(√(,10*x))

Solution

1. Rewrite the square root as a fractional exponent using the property √(n,a)=a(1/n)

(log_4)((10*x)(1/2))

2. Apply the power rule for logarithms, (log_b)(Mp)=p*(log_b)(M) to move the exponent to the front of the expression.

1/2*(log_4)(10*x)

3. Apply the product rule for logarithms, (log_b)(M*N)=(log_b)(M)+(log_b)(N) to separate the factors inside the logarithm.

1/2*((log_4)(10)+(log_4)(x))

4. Distribute the constant factor to each term in the expansion.

1/2*(log_4)(10)+1/2*(log_4)(x)

Final Answer

(log_4)(√(,10*x))=1/2*(log_4)(10)+1/2*(log_4)(x)

Want more problems? Check here!