Answer:
[tex]x\approx 0.8[/tex]
Step-by-step explanation:
The given expression is
[tex]2^{8x}=93[/tex]
To solve this we have to apply logarithms as follows
[tex]2^{8x}=93\\ln(2^{8x})=ln(93)[/tex]
Now, applying properties of logarithms, we have
[tex]ln(2^{8x})=ln(93)\\8x(ln2)=ln(93)\\x=\frac{ln93}{8(ln2)}\\ x\approx 0.8[/tex]
Therefore, the answer rounded to the nearest tenth is
[tex]x\approx 0.8[/tex]
Remember that you have to apply logarithms when the exponential equation cannot be expressed as equivalent powers.
