# Solving for x

#### nuckers

Can anyone help me out on this equation, i am doing exponents and logarithms, and can't seem to understand this, i get that you are supposed to make the base the same and then solve for x using the exponents, but how do you make the base the same in this function.

$$\displaystyle 7 ^3x+1=5^x$$

The 3x+1 is actually the exponent

#### e^(i*pi)

MHF Hall of Honor
Can anyone help me out on this equation, i am doing exponents and logarithms, and can't seem to understand this, i get that you are supposed to make the base the same and then solve for x using the exponents, but how do you make the base the same in this function.

$$\displaystyle 7 ^3x+1=5^x$$

The 3x+1 is actually the exponent
$$\displaystyle (3x+1)\ln(7) = x\ln(5)$$

You can distribute on the LHS as with any normal algebra

nuckers

#### harish21

Can anyone help me out on this equation, i am doing exponents and logarithms, and can't seem to understand this, i get that you are supposed to make the base the same and then solve for x using the exponents, but how do you make the base the same in this function.

$$\displaystyle 7 ^3x+1=5^x$$

The 3x+1 is actually the exponent
$$\displaystyle 7^{3x+1} = 5^x$$

$$\displaystyle log(7^{3x+1}) = log(5^x)$$

$$\displaystyle (3x+1) \mbox{log(7)} = x \mbox{log(5)}$$

$$\displaystyle \frac{3x+1}{x}= \frac{\mbox{log(5)}}{\mbox{log(7)}}$$

$$\displaystyle 3+ \frac{1}{x} = \frac{\mbox{log(5)}}{\mbox{log(7)}}$$

finish it..

nuckers

#### nuckers

$$\displaystyle 7^{3x+1} = 5^x$$

$$\displaystyle log(7^{3x+1}) = log(5^x)$$

$$\displaystyle (3x+1) \mbox{log(7)} = x \mbox{log(5)}$$

$$\displaystyle \frac{3x+1}{x}= \frac{\mbox{log(5)}}{\mbox{log(7)}}$$

$$\displaystyle 3+ \frac{1}{x} = \frac{\mbox{log(5)}}{\mbox{log(7)}}$$

finish it..
So i get -.46021234 for my final answer, does that sound right?

#### e^(i*pi)

MHF Hall of Honor
So i get -.46021234 for my final answer, does that sound right?
That's correct ^_^

You can test it by putting it into your original equation. If the two sides are equal than the answer is fine

nuckers