Solve for the exact value of x. log_(2)(8x)-2log_(2)(6)=3 Answer:

Apply power rule of logarithms: Apply the power rule of logarithms to the term 2log₂(6). The power rule states that a*log_b(c) = log_b(c^a). Therefore, we can rewrite 2log₂(6) as log₂(6^2). log₂(8x) - log₂(6^2) = 3Simplify term 6^2: Simplify the term 6^2. 6^2 equals 36, so the equation becomes: log₂(8x) - log₂(36) = 3Apply quotient rule of logarithms: Apply the quotient rule of logarithms to combine the logarithmic terms. The quotient rule states that log_b(a) - log_b(c) = log_b(a/c). Therefore, we can combine the logarithmic terms: log₂(8x/36) = 3Convert to exponential equation: Convert the logarithmic equation to an exponential equation. Using the definition of a logarithm, we can rewrite the equation as: 2^3 = 8x/36Calculate 2^3: Calculate 2^3. 2^3 equals 8, so the equation becomes: 8 = 8x/36Multiply by 36: Multiply both sides of the equation by 36 to solve for x. 36 * 8 = 8x 288 = 8xDivide by 8: Divide both sides of the equation by 8 to isolate x. 288/8 = x 36 = x

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for the exact value of
x.

log_(2)(8x)-2log_(2)(6)=3
Answer:

Solve for the exact value of $x$ . $\newline$ $\log _{2}(8 x)-2 \log _{2}(6)=3$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Calculus

Find derivatives of logarithmic functions

Full solution

Q. Solve for the exact value of

x

\newline

\log _{2}(8 x)-2 \log _{2}(6)=3

\newline

Answer:

Apply power rule of logarithms: Apply the power rule of logarithms to the term $2\log_2(6)$ . The power rule states that $a\log_b(c) = \log_b(c^a)$ . Therefore, we can rewrite $2\log_2(6)$ as $\log_2(6^2)$ . $\log_2(8x) - \log_2(6^2) = 3$
Simplify term $6^2$ : Simplify the term $6^2$ . $\newline$ $6^2$ equals $36$ , so the equation becomes: $\newline$ $log_2(8x) - log_2(36) = 3$
Apply quotient rule of logarithms: Apply the quotient rule of logarithms to combine the logarithmic terms. $\newline$ The quotient rule states that $\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)$ . Therefore, we can combine the logarithmic terms: $\newline$ $\log_2\left(\frac{8x}{36}\right) = 3$
Convert to exponential equation: Convert the logarithmic equation to an exponential equation. $\newline$ Using the definition of a logarithm, we can rewrite the equation as: $\newline$ $2^3 = \frac{8x}{36}$
Calculate $2^3$ : Calculate $2^3$ . $\newline$ $2^3$ equals $8$ , so the equation becomes: $\newline$ $8 = \frac{8x}{36}$
Multiply by $36$ : Multiply both sides of the equation by $36$ to solve for $x$ . $36 \times 8 = 8x$ $288 = 8x$
Divide by $8$ : Divide both sides of the equation by $8$ to isolate $x$ . $\frac{288}{8} = x$ $36 = x$