SOLUTION: find the value of x: log6 (5x+9)=4 a. 3 b. 817.4 c. 261 d. 257.4 I have no clue where to even start with this problem. ive tried pluging the answers in the calculator

Question 815940: find the value of x: log6 (5x+9)=4
a. 3
b. 817.4
c. 261
d. 257.4

I have no clue where to even start with this problem. ive tried pluging the answers in the calculator but havnt had luck with that
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Solving equations where the variable is in a logarithm usually starts with using algebra and/or properties of logarithms to transform the equation into one of the following forms:
log(expression) = number
or
log(expression) = log(other_expression)

Your equation is already in the first form. So we can skip to the next stage: Eliminate the logarithms. With the first form we rewrite the equation in exponential form. In general is equivalent to . Using this pattern on your equation we get:

which simplifies to:

Now we solve. Subtracting 9:

Divide by 5:

There are no fractions or mixed numbers in the given answers. So we convert the fraction to a decimal (by dividing 1287 by 5):

P.S. The reason your calculator didn't help was that it does not understand base 6 logarithms. Calculators usually "know" base 10 ("log") and base e ("ln") logarithms. To use your calculator on this you would have to use the base conversion formula, , to convert the base 6 log to a base 10 or base e log:

Now you could use trial and error of the possible answers to find out which one works.
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