SOLUTION: Can i please have a detailed answer step by step of the folllowing question: i) 9^x+5=50

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Question 179548This question is from textbook Core Mathematics 2
: Can i please have a detailed answer step by step of the folllowing question:
i) 9^x+5=50 This question is from textbook Core Mathematics 2

Found 2 solutions by josmiceli, nerdybill:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
9%5Ex+%2B+5+=+50
Subtract 5 from both sides
9%5Ex+=+45
Note that I can write 9%5Ex this way:
9%2A9%5E%28x+-+1%29
That's the same as saying 2%5E4+=+2%2A2%5E3
9%2A9%5E%28x+-+1%29+=+9%2A5
Divide both sides by 9
9%5E%28x+-+1%29+=+5
This is the same as
log%289%2C5%29+=+x+-+1
x+=+log%289%2C5%29+%2B+1
I can use the formula which says:
log%28b%2Cx%29+=+%28log%28k%2Cx%29%29+%2F+%28log%28k%2Cb%29%29 with k+=+10
log%289%2C5%29+=+log%285%29%2Flog%289%29
log%289%2C5%29+=+.69897+%2F+.95424
log%289%2C5%29+=+.73249
x+=+log%289%2C5%29+%2B+1
x+=+.73249+%2B+1
x+=+1.73249 answer
check:
9%5Ex+%2B+5+=+50
9%5E1.73249+%2B+5+=+50
45.00032+%2B+5+=+50
50.00032+=+50 close enough

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Like any other algebraic equation, solve for x by isolating it to one side of the equation.
.
9^x+5=50
subtract 5 from both sides:
9^x=45
take log_9 (log base 9) of both sides:
x = log_9(45)
x = log(45)/log(9)
x = 1.7325