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5^(x^2)<2^x solve giving your ans in terms of log

I got the ans x>log2/log 5, but the other ans is x<0. I dont understand how is x<0.

I got the ans x>log2/log 5, but the other ans is x<0. I dont understand how is x<0.

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#2

Think you made the classic mistake of dividing by x instead of taking everything to one side and factorising.

Edit. Are you sure the inequality in the original question is the right way round?

Edit. Are you sure the inequality in the original question is the right way round?

Last edited by dextrous63; 1 week ago

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(Original post by

Think you made the classic mistake of dividing by x instead of taking everything to one side and factorising.

**dextrous63**)Think you made the classic mistake of dividing by x instead of taking everything to one side and factorising.

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#4

(Original post by

No I did factorising .so 5^2x-2^x>0 and then applying log I get x>0 but the ans is x<0

**Shas72**)No I did factorising .so 5^2x-2^x>0 and then applying log I get x>0 but the ans is x<0

a + b = c does NOT mean log a + log b = log c

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(Original post by

Er, how did you apply logs after shifting everything over? By the looks of it, you seem to have made a common mistake:

a + b = c does NOT mean log a + log b = log c

**dextrous63**)Er, how did you apply logs after shifting everything over? By the looks of it, you seem to have made a common mistake:

a + b = c does NOT mean log a + log b = log c

Can you pls explain a bit more

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#7

(Original post by

So I did x^2log5-xlog2>0. Factorise you get x>0 and x> log2/log5

**Shas72**)So I did x^2log5-xlog2>0. Factorise you get x>0 and x> log2/log5

Sketch the quadratic curve y=log5 x^2 - log2 x, marking the roots on the x-axis.

When is the curve above the x-axis, and thus positive?

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(Original post by

OK. Your other post didn't make sense, hence my question. Back to the task.

Sketch the quadratic curve y=log5 x^2 - log2 x, marking the roots on the x-axis.

When is the curve above the x-axis, and thus positive?

**dextrous63**)OK. Your other post didn't make sense, hence my question. Back to the task.

Sketch the quadratic curve y=log5 x^2 - log2 x, marking the roots on the x-axis.

When is the curve above the x-axis, and thus positive?

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#9

(Original post by

How do you do that? So you have to calculate the values of log 5 and log 2

**Shas72**)How do you do that? So you have to calculate the values of log 5 and log 2

Sketch the curve, marking these two point on the x-axis.

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(Original post by

No. You know it's a quadratic, and factorising will give x(log5 x - log2), so the roots are 0 and log2/log5.

Sketch the curve, marking these two point on the x-axis.

**dextrous63**)No. You know it's a quadratic, and factorising will give x(log5 x - log2), so the roots are 0 and log2/log5.

Sketch the curve, marking these two point on the x-axis.

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#11

(Original post by

So I marked 0 and 0.4 on x axis

**Shas72**)So I marked 0 and 0.4 on x axis

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**dextrous63**)

No. You know it's a quadratic, and factorising will give x(log5 x - log2), so the roots are 0 and log2/log5.

Sketch the curve, marking these two point on the x-axis.

(Original post by

Sketch the curve. When does it go above the x-axis?

**dextrous63**)Sketch the curve. When does it go above the x-axis?

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(Original post by

What does a quadratic curve look like? Where does it pass through the x-axis?

**dextrous63**)What does a quadratic curve look like? Where does it pass through the x-axis?

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#15

(Original post by

Quadratic curve is a parabola . It passes x axis when x=0 and y=0

**Shas72**)Quadratic curve is a parabola . It passes x axis when x=0 and y=0

With that in mind, either download the Desmos app on your phone, or go to geogebra on your laptop/phone/tablet and get it to draw the graph y=log5 x^2 - log2 x (you might find it easier to use decimal values for the logs) and look for where the graph is positive (above the x-axis).

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(Original post by

I think there are some holes in your understanding which need dealing with.

With that in mind, either download the Desmos app on your phone, or go to geogebra on your laptop/phone/tablet and get it to draw the graph y=log5 x^2 - log2 x (you might find it easier to use decimal values for the logs) and look for where the graph is positive (above the x-axis).

**dextrous63**)I think there are some holes in your understanding which need dealing with.

With that in mind, either download the Desmos app on your phone, or go to geogebra on your laptop/phone/tablet and get it to draw the graph y=log5 x^2 - log2 x (you might find it easier to use decimal values for the logs) and look for where the graph is positive (above the x-axis).

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**dextrous63**)

I think there are some holes in your understanding which need dealing with.

With that in mind, either download the Desmos app on your phone, or go to geogebra on your laptop/phone/tablet and get it to draw the graph y=log5 x^2 - log2 x (you might find it easier to use decimal values for the logs) and look for where the graph is positive (above the x-axis).

Its above x axis only when x<0

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