Solve: a) `log_2.17(5x-1)−log_2.17(x+7)=0` b) `2e^x+2=5` c) `5+2ln(x)=4`
Since the two logarithms have same base, express the right side as one logarithm.To do so, apply the quotient rule` log_b(M/N)=log_bM-log_bN` .
Then, convert to it to exponential equation. The equivalent exponential equation of `log_b M=a` is
Now that the equation has no more logarithm, proceed to solve for x.
Hence, the solution to the given equation is `x=2` .
First, isolate e^x.
To remove the x in the exponent, take the logarithm of both sides.
`x ln e=ln(3/2)`
Hence, the solution to the equation is `x=ln (3/2)` .
First, isolate lnx.
Then, convert to its equivalent exponential equation.
Hence, the solution to the equation is `x=1/e^(1/2)` .