3^x+1=5^x-4 what is x?

Hello from MrBillDoesMath!

Answer: 14.75330052 ...

Discussion: Per the author the equation should be interpreted as

3 ^ (x+1) = 5^ (x-4)

NOT as (3^x) + 1 = (5^x) - 4

Rewrite the equation to pull out the constant terms:

3^ (x+1) = 3^x * 3^1 = 3^x * 3 = 5^x * (5^-4)

so 3^x * 3 = 5^x * (5^-4)

Divide both sides by 3 to get

3^x * = 5^x * ((5^-4) / 3)

Divide both sides by 5^x to get

(3/5) ^ x = (1/625 * 1/3) = 1/1875

Take the base 10 logarithm (is this middle school math?) of each side

x * log (3/5) = log (1/1875) or (taking log. bring exponent down)

x = log (1/1875) / log (3/5)

so

x = (-3.273001272) / - 0.22184875

which gives x as approx 14.75

I suspect there is still something wrong in the problem statement as I'm skeptical that this is middle level math.

Regards, MrB

3^x+1=5^x-4 what is x? X=3

3^x+1=5^3-4