Solve for the exact value of x. log_(7)(8x)+2log_(7)(8)=2 Answer:

Question

Solve for the exact value of  x.  log_(7)(8x)+2log_(7)(8)=2 Answer:

Bytelearn · Accepted Answer

Apply Power Rule: Apply the power rule of logarithms to the second term. The power rule states that a*log_b(c) = log_b(c^a), where a is a real number, b is the base of the logarithm, and c is the argument of the logarithm. We can apply this rule to the second term of the equation to simplify it. 2log_(7)(8) = log_(7)(8^2) = log_(7)(64)Rewrite Equation: Rewrite the equation using the result from Step 1. The equation now becomes: log_(7)(8x) + log_(7)(64) = 2Combine Logarithmic Terms: Combine the logarithmic terms using the product rule. The product rule of logarithms states that log_b(m) + log_b(n) = log_b(m*n), where b is the base of the logarithm, and m and n are the arguments. We can combine the two logarithmic terms on the left side of the equation. log_(7)(8x * 64) = 2Simplify Argument: Simplify the argument of the logarithm. Multiply 8x by 64 to get the new argument of the logarithm. log_(7)(512x) = 2Convert to Exponential: Convert the logarithmic equation to an exponential equation. The equation log_b(m) = n can be rewritten as b^n = m. We will use this property to solve for x. 7^2 = 512xSolve for x: Solve for x. Divide both sides of the equation by 512 to isolate x. x = 7^2 / 512 x = 49 / 512

Solve for the exact value of $x$ . $\newline$ $\log _{7}(8 x)+2 \log _{7}(8)=2$ $\newline$ Answer:

Full solution

More problems from Find derivatives of logarithmic functions

Related topics

Solve for the exact value of x x x.\newlinelog⁡7(8x)+2log⁡7(8)=2 \log _{7}(8 x)+2 \log _{7}(8)=2 log7​(8x)+2log7​(8)=2\newlineAnswer:

Solve for the exact value of $x$ . $\newline$ $\log _{7}(8 x)+2 \log _{7}(8)=2$ $\newline$ Answer: