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#1
0.8^(1-3x)>10 (greater than OR EQUAL TO not just greater than)

I used base of 10

log0.8 ^(1-3x)> log10
1-3x(log0.8)> log10
1-3x> (log10)/(log0.8)
-3x> (log10/log0.8)-1
x<((log10/log0.8)-1)/3
x< 3.77 (Less than OR EQUAL TO)

Could someone please tell me where I've gone wrong? I'm pretty sure the answer is x>3.77 rather than x<3.77. Was I not meant to flip the inequality when dividing by -3?
Thanks
0
6 years ago
#2
By computing log(0.8), you will find out that it is negative. Hence, you also flip the inequality sign when dividing by log(0.8) to achieve your required result.
0
6 years ago
#3
(Original post by Johnpeters)
0.8^(1-3x)>10 (greater than OR EQUAL TO not just greater than)

I used base of 10

log0.8 ^(1-3x)> log10
1-3x(log0.8)> log10
1-3x> (log10)/(log0.8)
-3x> (log10/log0.8)-1
x<((log10/log0.8)-1)/3
x< 3.77 (Less than OR EQUAL TO)

Could someone please tell me where I've gone wrong? I'm pretty sure the answer is x>3.77 rather than x<3.77. Was I not meant to flip the inequality when dividing by -3?
Thanks
Log0.8 is a negative number , should have flipped the sign there too

Log(x), where x < 1 is negative, remember the log graph?
0
#4
Thank you, would never have thought of that!

And no I've never seen a log graph? We've done exponential graphs, is it anything to do with them?
0
6 years ago
#5
(Original post by Johnpeters)
Thank you, would never have thought of that!

And no I've never seen a log graph? We've done exponential graphs, is it anything to do with them?
0
6 years ago
#6
(Original post by Johnpeters)
Thank you, would never have thought of that!

And no I've never seen a log graph? We've done exponential graphs, is it anything to do with them?

(Original post by krisshP)
Every log function is the inverse of a corresponding exponential function for some base. If you've seen an exponential graph then you can get the inverse (log) graph by reflecting in y = x.

And whatever base you're using log 1 = 0 with log x < 0 when x < 1
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