Final answer to the problem
$x=\frac{16}{15}$
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Step-by-step Solution
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1
The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$
$\log_{4}\left(\frac{x}{x-1}\right)=2$
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$\log_{4}\left(\frac{x}{x-1}\right)=2$
Learn how to solve problems step by step online. Solve the logarithmic equation log4(x)-log4(x+-1)=2. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Rewrite the number 2 as a logarithm of base 4. For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \log(a)=\log(b) then a must equal b. Calculate the power 4^2.
Final answer to the problem
$x=\frac{16}{15}$
Exact Numeric Answer
$x=1.0666667$
