# What is the value of x? Find it from the picture given below:

#### Abu Sayeed Mahi

##### New member

What is the value of x?

#### lex

##### Full Member
Is the topic related to numerical solutions of equations?
Otherwise, I wonder is there a mistake in the statement.

#### HallsofIvy

##### Elite Member
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 $$\displaystyle log_2(2^{2x+2}+ 2^2)$$.

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#### Eugenio

##### New member
The LHS is 3. The RHS is 6 when x = 0 and 0 when x = -1. The solution is between -1 and 0. You need a numerical approach.

#### Jomo

##### Elite Member
log base ab of ac=c/a.
This fact above will tell you exactly what the lhs equals.

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