# If Logb(x) = 0.8, solve for Logb(x)(x^1/3)

1. Jan 10, 2012

### srizen

1. The problem statement, all variables and given/known data

i got a question on a quiz, but i really did not know how to solve it. the question that was stated was:
if $\log_b x =0.8$

Solve for
$\log_b x(\sqrt[3]{x})$

3. The attempt at a solution

basically what i attempted to do was
b0.8 = x

Logb x + Logb 3√x

Logb x + 1/3Logb x

0.8 + 1/3Logb x ?

EDIT:
picture attachment
formatting

Last edited: Jan 10, 2012
2. Jan 10, 2012

### Staff: Mentor

You're not solving for anything - you are evaluating this expression.

In any case, is that what you're working with?
$$log_b(x \sqrt[3]{x})$$

If so, that's different from what you wrote.

3. Jan 10, 2012

### srizen

hmm, let me scan it, i dont know how to do all these math symbols

#### Attached Files:

• ###### maths.jpg
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4. Jan 10, 2012

I assume you mean $log$$_{b}$$x$$\sqrt[3]{x}$?

Try to get it so you have $klog$$_{b}$$x$, $k$ $constant$

Last edited: Jan 10, 2012
5. Jan 10, 2012

### eumyang

Try to rewrite the expression
$\log_b(x \sqrt[3]{x})$
as a single power, ie.
$\log_b(x^a)$
for some number a. You'll then need the power property of logarithms.

6. Jan 10, 2012

### srizen

that would be simple, but its
$\log_b x( \sqrt[3]{x})$

7. Jan 10, 2012

Use the relationship
$x$$^{\frac{1}{a}}$ = $\sqrt[a]{x}$

And $x^{a}$$x^{b}$ = $x^{a+b}$

8. Jan 10, 2012

### Mentallic

If it's supposed to be in that form as the question asks, which I suppose should mean

$$(\log_bx)(\sqrt[3]{x})$$

Then simply plug in 0.8 into the first bracket since you're already given that, and solve for x in $\log_bx=0.8$ to find $\sqrt[3]{x}$

9. Jan 10, 2012

### srizen

yea thats my question, how do you solve for x

when ur given 2 variables?

b is not given :S

heres what im doing so far:

b0.8 = x

Logb x + Logb 3√x

Logb x + 1/3Logb x

0.8 + 1/3Logb x ?

Last edited: Jan 10, 2012
10. Jan 10, 2012

That's right. You know $log_{b}x$ = 0.8, so sub that in.

11. Jan 10, 2012

### srizen

the only problem is that, the answer should be 1.07 =/

12. Jan 10, 2012

### Mentallic

Ok so it IS meant to be $$log_b(x\sqrt[3]{x})$$ as opposed to $$(log_bx)\cdot \sqrt[3]{x}$$

Yes, the answer is 1.07, what's the problem? 0.8 + 1/3*0.8 = ?

13. Jan 10, 2012

### srizen

ohh, ok i see my mistake now :S

this is such an easy problem, i was jus over thinking >_<

14. Jan 10, 2012

### Staff: Mentor

Whoever wrote this problem did not communicate the problem in a clear way. The only way we could understand what was written was to reverse-engineer the solution. The problem should have been written so that it was clear what the argument of the log function was.

15. Jan 10, 2012

### Mentallic

Yep

I was about to ask for the solution if the OP didn't already provide it. This confusion was unnecessarily getting out of hand...

edit: the answer was written in the attachment. To be honest, it looked like effort to try and understand what was happening on that page so I gave up!