Solve each logarithmic equation in Exercises 49–92. Be sure to re...

Question

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. log4(3x+2)=3

Accepted Answer

Hey everyone here we are asked to solve the logarithmic equation of log base eight of five. X plus four is equal to four. Now to solve this equation we need to recall that log base B of X is equal to A. And this equation converts to X. Is equal to B to the power of A. So we can see that our given equation is in this log base B of X is equal to a format. So we can identify our B. X. And A values. So here we can see that B is equal to AIDS. And then we can see that our X. Is this five X plus four and then our A value is just four. And with this we can plug in these values into this converted form. So we have X. Which is five X plus four is equal to B which is eight to the power of four. So now we can start simplifying and solve for X. So we have five X plus four is equal to 4096. We then subtract four from both sides giving us five X is equal to 4092. We then get X alone by dividing both sides by five. And we see that X is equal to 4092 divided by five which in decimal form is equal to 818.40. This leaves us with answer choice D. Thanks for watching. I hope you found this video helpful and I'll see you again next time

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