Question

question 23, *7.5. solve the equation. log 16(4x - 1) = 1/4 x = (simplify your answer.)

Explanation:

Step1: Convert to exponential form

By the definition of logarithms, if $\log_{a}b = c$, then $b=a^{c}$. So, $4x - 1=16^{\frac{1}{4}}$.

Step2: Calculate $16^{\frac{1}{4}}$

We know that $16 = 2^4$, so $16^{\frac{1}{4}}=(2^4)^{\frac{1}{4}} = 2$. Then the equation becomes $4x - 1=2$.

Step3: Solve for $x$

Add 1 to both sides: $4x=2 + 1=3$. Then divide both sides by 4, we get $x=\frac{3}{4}$.

Answer:

$\frac{3}{4}$