SOLUTION: I have problems solving the following equation Problem : 19^(1-x)= 12 In terms of log or ln or correct to four decimal places

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Question 193107: I have problems solving the following equation
Problem :
19^(1-x)= 12
In terms of log or ln or correct to four decimal places
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
19%5E%281-x%29=+12 Start with the given equation.


log%2810%2C%2819%5E%281-x%29%29%29=+log%2810%2C%2812%29%29 Take the log base 10 of both sides


%281-x%29log%2810%2C%2819%29%29=+log%2810%2C%2812%29%29 Pull down the exponent


1-x=log%2810%2C%2812%29%29%2Flog%2810%2C%2819%29%29 Divide both sides by log%2810%2C%2819%29%29.


1-x=log%2819%2C%2812%29%29 Use the change of base formula to rewrite the right side


-x=log%2819%2C%2812%29%29-1 Subtract 1 from both sides.


x=-log%2819%2C%2812%29%29%2B1 Multiply EVERY term by -1 to isolate "x"


So the solution is x=-log%2819%2C%2812%29%29%2B1 which approximates to