Question

Explain how to solve 3^x-4=6 using the change of base formula (x minus 4 is the exponent not just x) HELP!!!

Answer 1

x ≈ 5.63093

Explanation:

Taking the log to the base 3, you have ...

x -4 = log₃(6)

Using the change of base formula, this becomes ...

x -4 = log(6)/log(3) . . . . . . where the log is to any consistent base

x = 4 + log(6)/log(3) = 4 +0.77815/0.47712

x ≈ 5.63093

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The "change of base" formula tells you ...

`\log_n{m}=\frac{\log{m}}{\log{n}}`

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In general, function arguments need parentheses if there is the least possibility of ambiguity. Exponents need parentheses if any arithmetic operation is involved. You equation is better written as ...

3^(x-4) = 6

or typeset as ...

`3^(x-4)=6`