Can somebody help me find the value for 'X' in this equation? 10^x-7 = 10^3x+8

Question

johnweldon1993 · Answer

Since these "exponents" both have the same base...we can ignore that 10....and just set the exponents equal to each other

$$\large x - 7 = 3x + 8$$

Because when we find out what 'x' equals we can make both 10^(that) and they will also be equal

johnweldon1993 · Answer

Assuming this is

$$\large 10^{x - 7} = 10^{3x + 8}$$?

anonymous · Answer

Yes sir.

johnweldon1993 · Answer

Alright...so yes all we need to do is solve that top equation

$$\large x - 7 = 3x + 8$$
subtract 8 from both sides and subtract x from both sides
$$\large 2x = -15$$
$$\large  x = ?$$

anonymous · Answer

X would be -7.5 is that correct?

johnweldon1993 · Answer

Correct...now lets see if it IS correct

$$\large 10^{(-7.5 - 7)} = 10^{3(-7.5) + 8}$$
$$\large 10^{-14.5} = 10^{-14.5}$$ 
$$\large \color \red{\checkmark}$$

anonymous · Answer

Thank you so much for the help.

johnweldon1993 · Answer

No problem!