Abu Sayeed Mahi
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What is the value of x?
What is the value of x? Find it from the picture given below:
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What is the value of x?
HallsofIvy
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A logarithm is the inverse function to the exponential. For any a and x, \(\displaystyle log_a(a^x)= x\).
\(\displaystyle 8= 2^3\) so \(\displaystyle \sqrt{8}= 2^{3/2}\) and \(\displaystyle \frac{1}{\sqrt{8}}= \left(\frac{1}{\sqrt{2}}\right)^3\).
\(\displaystyle 4= 2^2\) so \(\displaystyle 4^{x+1}= (2^2)^{x+1}= 2^{2(x+1)}= 2^{2x+2}\) so \(\displaystyle log_2(4^{x+ 1})=2x+ 2\).
It is the last logarithm that is the problem. There is no way to simplify \(\displaystyle log_2(2^{2x+2}+ 2^2)\).
\(\displaystyle 8= 2^3\) so \(\displaystyle \sqrt{8}= 2^{3/2}\) and \(\displaystyle \frac{1}{\sqrt{8}}= \left(\frac{1}{\sqrt{2}}\right)^3\).
\(\displaystyle 4= 2^2\) so \(\displaystyle 4^{x+1}= (2^2)^{x+1}= 2^{2(x+1)}= 2^{2x+2}\) so \(\displaystyle log_2(4^{x+ 1})=2x+ 2\).
It is the last logarithm that is the problem. There is no way to simplify \(\displaystyle log_2(2^{2x+2}+ 2^2)\).
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Steven G
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log base ab of ac=c/a.
This fact above will tell you exactly what the lhs equals.
This is a math help forum where we help students solve their problems. We do not solve problems for students.
Since math is not a spectator sport we want you to be involved in solving your problem.
This fact above will tell you exactly what the lhs equals.
This is a math help forum where we help students solve their problems. We do not solve problems for students.
Since math is not a spectator sport we want you to be involved in solving your problem.