how to calculate the value of 'x', If 16^x = 2?

How to calculate the value of 'x', If 16^x = 2?
Have you tried anything? If yes, then please show us as this is the forum policy--to help students with homework but not do it for them.

I'll give you some hints: 4^(3/2) is asking two questions. The first is what times itself 2 times give you 4? The answer to that question is 2. Now multiply that answer by itself 3 times to get the final answer of 8.

25^(1/2)---1st find what times itself 2 times give you 25, That answer is 5. Now raise 5 to the 1st power (or multiply 5 by itself 1 time) and the final answer is 5.

Show us your work with your problems. Thanks!
 
Have you tried anything? If yes, then please show us as this is the forum policy--to help students with homework but not do it for them.

I'll give you some hints: 4^(3/2) is asking two questions. The first is what times itself 2 times give you 4? The answer to that question is 2. Now multiply that answer by itself 3 times to get the final answer of 8.

25^(1/2)---1st find what times itself 2 times give you 25, That answer is 5. Now raise 5 to the 1st power (or multiply 5 by itself 1 time) and the final answer is 5.

Show us your work with your problems. Thanks!
I understand what you mean. 4^3/2 = 4^(1/2)×3 = (√4)^3 = (2)^3 = 8 but my question is different here. As we know 5^x = 25 so x = 5. so how to calculate the value of 'x' if 16^x = 2?
 
I understand what you mean. 4^3/2 = 4^(1/2)×3 = (√4)^3 = (2)^3 = 8 but my question is different here. As we know 5^x = 25 so x = 5. so how to calculate the value of 'x' if 16^x = 2?
\(\displaystyle 16^x = 2 \implies log_2(16^x) = log_2(2) = 1 \implies WHAT?\)
 
As you said, I did below
2^4 = 2^1 now what?

You need to use the facts that 16 = 2^4 and 2 = 2^1 to rewrite the original equation so that you can apply this convenient rule: if ax = ay, then x = y.
 
As you said, I did below
2^4 = 2^1 now what?

That's not quite what I said.

What I said was to replace 16 in your equation 16^x = 2 with 2^4:

(2^4)^x = 2^1

Now simplify the left side, and see what happens.
 
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As you said, I did below
2^4 = 2^1 now what?
No. The 24 accounts only for the 16, not for the variable. Restate the entire equation:

. . . . .(24)x = 21

Then use exponent rules to condense the power on the left-hand side. Then equate the two powers, and divide through to find the value of the variable. ;)
 
No. The 24 accounts only for the 16, not for the variable. Restate the entire equation:

. . . . .(24)x = 21

Then use exponent rules to condense the power on the left-hand side. Then equate the two powers, and divide through to find the value of the variable. ;)
I can't believe how I forgot to explain it that way. I need to get back into teaching again as this is always how I did these problems. Thanks for reminding me.
 
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