Question

Solve the exponential equation 9^8x = 27

Answer 1

Answer:

$x=\frac{3}{16}$

Step-by-step explanation:

Given : Exponential function $9^{8x}=27$

We have to solve the given exponential equation.

Consider the given exponential function $9^{8x}=27$

$\mathrm{Convert\:}9^{8x}\mathrm{\:to\:base\:}3$

$9^{8x}=\left(3^2\right)^{8x}$

Function becomes,

$\left(3^2\right)^{8x}=27$

Convert 27 to base 3, we have,

$\left(3^2\right)^{8x}=3^3$

Apply exponent rule, $\left(a^b\right)^c=a^{bc}$

We have, $3^{2\cdot \:8x}=3^3$

$\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)$

We have,

$2\cdot \:8x=3$

Simplify, we have,

$16x=3$

Thus, $x=\frac{3}{16}$

Answer 2

The answer is x=3/16