Which planet search technique is currently best suited to finding earth-like planets?

The planet search technique currently best suited to find Earth-like planets is gravitational microlensing.

Explanation:

Gravitational microlensing

When a foreground star (lensing star) passes in front of a background star (source star), due to its gravitational field it warps space and magnifies the light coming from the source star. If the lensing star has a planet orbiting near, the planet's gravity also bends light and intensifies this effect. What is observed is a sharp increase in brightness in the otherwise regular pattern of the microlensing event. Certain characteristics of the planet like its total mass, orbit and period can be obtained from said pattern.

This technique is independent of the wavelength of the source star which makes it suitable for any kind of electromagnetic radiation.

Microlensing is suitable to find smaller, rocky planets like Earth because is more sensitive to planets whose orbits are further apart from the parent star.

Other indirect detection techniques like the radial velocity method and the transit method are biased towards massive gaseous planets that orbit very close to their parent star.

The radial velocity method makes use of the Doppler effect, that involves the change in frequency of a wave depending on the relative movement of the observer and the wave source. This relative motion, that should be in the line that joins the wave source and the observer, is called the radial motion. That is why the velocity of this motion is called the radial velocity. If a star is moving towards Earth the light waves reach us faster. We say the spectrum is blue shifted because the color blue has the shortest wavelength in the visible spectrum. If the star is moving away from the Earth the light waves reach us later and the wavelength becomes larger. We say the spectrum is red shifted because the color red has the longest wavelength. If a planet is orbiting  star there will be stellar motion caused by the tug of the planet, the doppler shift allow us to detect this subtle motion. Is currently unsuitable to detect small, rocky planets like Earth because maasive planets orbiting very close to their stars create a larger and easily to note spectral shift.Transit method : if a planet crosses in front of the star it orbits, the star brightness tenporarily decreases a little. This method is also unsuitable because with large and gaseous planets the drop in brightness iseasier to spot.

45 is the correct answer