SOLUTION: By taking logarithm base 10 of both sides, solve the index equation correct to 4 significant figures. 7^(1-x)= 6*5^(x-3)

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Question 1178840: By taking logarithm base 10 of both sides, solve the index equation correct to 4 significant figures.
7^(1-x)= 6*5^(x-3)


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
7%5E%281-x%29=+6%2A5%5E%28x-3%29

log%287%5E%281-x%29%29=+log%286%2A5%5E%28x-3%29%29

log%287%5E%281-x%29%29=+log%286%29%2Blog%285%5E%28x-3%29%29

%281-x%29log%287%29=log%286%29%2B+%28x-3%29log%285%29

log%287%29-x%2Alog%287%29=log%286%29%2B+xlog%285%29-3log%285%29

log%287%29%2B3log%285%29-log%286%29=+xlog%285%29+%2Bx%2Alog%287%29

log%287%29%2B3log%285%29-log%286%29=+x%28log%285%29+%2Blog%287%29%29

x=%28log%287%29%2Blog%285%5E3%29-log%286%29%29%2F%28log%285%29+%2Blog%287%29%29

x=log%28%28%287%2A5%5E3%29%2F6%29%29%2Flog%285%2A7%29%29

x=log%28%28875%2F6%29%29%2Flog%2835%29%29-> exact solution

or
x=1.4014