# Solve 2^3x+1=32: Find X Using Logs

• MHB
• blackfriars
In summary, to solve the equation 2^{3x+1}=32, we can take the logarithm of both sides to get 3x+1=5, and then solve for x by subtracting 1 and dividing by 3. The final answer is x = 4/3.
blackfriars
hi could anyone show me the steps for solving this equation
i thought it was to be solved by logs
find X if 2^3x+1=32

blackfriars said:
hi could anyone show me the steps for solving this equation
i thought it was to be solved by logs
find X if 2^3x+1=32

Is the equation:

$$\displaystyle 2^{3x}+1=32$$

Or:

$$\displaystyle 2^{3x+1}=32$$

I suspect it is the latter, but I want to be sure first. :)

the answer i got for X was 5 just by using algebra
yes it is the latter equation
thanks

$$2^{3x+1}=32=2^5$$

$$3x+1=5\implies x=\frac43$$

Could you show steps for solving for x
Thanks

- - - Updated - - -

Yeah i got it now cheers mate

$$3x+1=5$$

Subtract $1$ from both sides:

$$3x+1-1=5-1$$

$$3x=4$$

Divide both sides by $3$:

$$x=\frac43$$

## 1. How do you solve 2^3x+1=32 using logs?

To solve this equation, we will use logarithms to isolate the variable x. First, we will take the logarithm of both sides of the equation. This will give us log(2^3x+1) = log(32). Then, we can use the logarithm property log(a^b) = b*log(a) to simplify the equation to 3x+1 = log(32). Finally, we can solve for x by subtracting 1 from both sides and dividing by 3, giving us x = (log(32)-1)/3.

## 2. Why do we need to use logarithms to solve this equation?

We need to use logarithms because the variable x is in the exponent of the base 2. By taking the logarithm of both sides, we can bring the variable down from the exponent and make it easier to solve for.

## 3. What is the purpose of using the logarithm property in this equation?

The logarithm property allows us to simplify the equation by bringing the variable down from the exponent. This makes it easier to solve for x and find the solution to the equation.

## 4. Can this equation be solved without using logarithms?

Yes, this equation can be solved without using logarithms. However, it would involve more complex algebraic manipulations and may be more difficult to solve compared to using logarithms.

## 5. Are there any restrictions on the values of x in this equation?

Yes, there are some restrictions on the values of x in this equation. Since logarithms are only defined for positive numbers, the expression 2^3x+1 must be positive. This means that the value of x must be greater than -1/3. Additionally, the base of the logarithm cannot be 0 or 1, so the value of x cannot be equal to 0. Therefore, the solution to this equation is x = (log(32)-1)/3, where x > -1/3 and x ≠ 0.

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