Using logarithm to calculate the following leaving your answer correct to two significant figures log 3 to the power x is equal to log 5

The equation is given as $\log 3^x = \log 5$.
Using the logarithm property $\log a^b = b \log a$, we can rewrite the left side:

$$x \log 3 = \log 5$$

To find $x$, divide both sides by $\log 3$:

$$x = \frac{\log 5}{\log 3}$$

Using a calculator for base-10 logarithms:

$$\log 5 \approx 0.69897$$ $$\log 3 \approx 0.47712$$

Now, substitute these values into the equation for $x$:

$$x = \frac{0.69897}{0.47712}$$ $$x \approx 1.46497$$

The first significant figure is 1, and the second is 4. The digit following the second significant figure is 6, which is 5 or greater, so we round up the second significant figure.

$$x \approx 1.5$$

The value of $x$ correct to two significant figures is $\boxed{1.5}$.