Need help solving exponential expression

[Guest]

I am a bit lost in solving this expression. I'm obviously missing a trick or manipulation which is required, but simply cannot grasp what I'm missing.
Can you point me in the right direction?

The problem is this:
If 6^x = 5

Solve
18^x / 2^-x

I get to this point, but then get stuck:
18^x / 2^-x
= (3[*]6)^x/(1/2^x)
= 3^x[*]6^x[*]2^x
= 3^x[*]5[*]2^x
=??

This is where I get stuck. There's obviously some conversion which I'm not aware of.
Any help?

[Guest]

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[akayfman]

To solve the expression 18x / 2-x, we can follow these steps:

Start with the given equation: 6x = 5
Solve for x by dividing both sides by 6: x = 5/6
Now, let’s proceed to solve the expression using the value of x we found.

Substitute x = 5/6 into the expression: 18x / 2-x = 18(5/6) / 2 - (5/6)

Now, simplify the expression step by step:

Multiply 18 and (5/6): = (18 * 5) / 6 = 90 / 6 = 15

Substitute x = 5/6 into the denominator: = 2 - (5/6) = (12/6) - (5/6) = 7/6

Now, divide the numerator by the denominator: 15 / (7/6)

To divide by a fraction, we can multiply by its reciprocal: 15 (6/7) = *90 / 7

So, the solution to the expression 18x / 2-x when x = 5/6 is 90 / 7.

[Guest]

To solve the expression18x/2−x, we can follow these steps:
• Start with the given equation:
6x=5
• Solve for x by dividing both sides by 6:
x=5/6
• Now, let’s substitute x=5/6 into the expression 18x/2−x:
18(5/6)/2(5/6)
Simplify the expression step by step:
• First, calculate the numerator:
18(5/6)=(18×5)/6=90/6=15
• Next, simplify the denominator:
2−5/6=(12/6)−(5/6)=(12−5)/6=7/6
• Now, divide the numerator by the denominator:
15/(7/6)
• To divide by a fraction, multiply by its reciprocal:
15×6/7=(15×6)/7=90/7
Therefore, the solution to the expression 18x/2−x when x=5/6 is 90/7.

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