# Logs.

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Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

7^x = 6^(x + 7)
this is how far I got: x log 7/x log 7= x+7 log 6/log 7, I am not too sure what to do next.

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.

log9 11 + log9 x = 1 ( I don't understand what to do)

log3(x + 5) = 2 + log3(x - 1) (For this problem I know I have to combine 2(x-1), but I don't know what to do next)

log10(x - 30) = 3 - log10 x (For this problem, I thought about solving it like x-30=3x, but I tried that I didn't get the answer I was suppose to)

• Logs. -

Please limit yourself to one question per post. Here is how to do two of them

2. log9 11 + log9 x = 1

(log9 means log to base 9)

log9 (11x) = 1 = log9 9
(The log to any base of the base itself is 1)

11x = 9

x = 9/11

3. log3(x + 5) = 2 + log3(x - 1)
log3 [(x+5)/(x-1)] = 2 = log3 (9)
(since 3^2 = 9, log3 9 = 2)
(x+5)/(x-1) = 9
x+5 = 9x - 9
Now solve for 9

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