7^(x – 2) = 12^x

x ≈ 3.28

x ≈ 0.31

x ≈ –7.22

x ≈ –0.14

Question

7^(x – 2) = 12^x 

x ≈ 3.28 

x ≈ 0.31 

x ≈ –7.22 

x ≈ –0.14

mandre · Answer

Just substitute each number and see which one works.

campbell_st · Answer

you can use logs... base e or base 10 doesn't matter and apply the log laws for powers

$$\log(a^b) = b \log a$$

applying the log law above 

$$(x-2)\ln(7) = xln(12)$$

distribute the left hand side

$$xln(7) - 2\ln(7) = xln(12)$$

collect like terms 

$$-2 \ln(7) = x \ln(12) -x \ln(7)$$

factor the right hand side

$$-2 \ln(7) = x(\ln(12) - \ln(7))$$

apply the log law for division 

$$\log(\frac{a}{b}) = \log(a) - \log(b)$$

so 

$$-2 \ln(7) = x(\ln(\frac{12}{7})$$

hopefully you can solve for x now...