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. log3(x+4)=−3

Accepted Answer

Hey everyone here we are asked to solve the following logarithmic equation of log base seven of X plus one is equal to negative two. Now to solve this equation we first need to recall that log base B of X is equal to a converts to the equation X is equal to B to the power of A. And now with this information we want to know our A. B. And X values from the given equation so we can rewrite the given equation. And we also need to note that this given equation is in the log base B of X is equal to a format. So our A here is negative two, B is seven and X is X plus one. And now using this information we can rewrite the given equation into the converted equation format. So we have X which is X plus one is equal to B which is seven to the power of negative two. And now we want to simplify this equation and solve for X. So we have X plus one is equal to. Now if we recall the exponential rule for a negative exponents, we know that seven to the power of negative two is equivalent to one divided by seven to the power of two. And then so simplifying further, we have X plus one is equal to one divided by 49. And now we can subtract one from both sides. So we have X is equal to negative 48 49 which has a decimal approximation of negative 0. and now we are left with answer choice C. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

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