Struggling with Logarithms

[Jesrose]

Was given a list of exponential equations which I could solve fairly easily with other methods, but when I checked the key I don't understand the method used.

For example: in the equation 3^2x=81, the explanation for the solution of x = 2 was written as 2x log(3 /(2 log(3) = log81 /(2 log(3) with no other explanation.

As far as I understand, 3^2x = 81 in log form is 2x= log(3 81, and I can't figure out how that was translated into the explanation given by the key. What steps am I missing?

 

[lookagain]

For example: in the equation 3^2x=81, the explanation for the solution of x = 2 was . . .

As far as I understand, 3^2x = 81 in . . .

This is written incorrectly. The exponent, in this case, must be inside grouping symbols:

3^(2x) = 81

You could skip the use of logarithms, because 3 and 81 share the common base of 3.

3^(2x) = 3^4

Because the sides are equal and the bases are equal, equate the exponents:

2x = 4

x = 2

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OR

3^(2x) = 81

3^(2x) = 3^4

log[3^(2x)] = log(3^4)

(2x)log(3) = (4)log(3)

Divide each side by (2)log(3):

x = 2

 

[Steven G]

As lookagain stated you should not use logs in this problem as you should know that 3^4=81.

But if you insist: 3^2x = 81 --> log₃81 = 2x, Since by definition a^b=c is log_ac=b.

log₃81 = log(81)/log(3) = 2x. Then x = log(81)/(2log(3)) = 2